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The subjects and authors, so far as selected, are as follows : 

VOLUMES PUBLISHED. 

Zoology of the Vertebrate Animals. By A. Macalistkr, M.D., 
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Brown University. i6mo. 60 cents. 

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Astronomy. By R. S. Ball, LL.D., F.R.S., Astronomer Royal for 
Ireland. Specially Revised for America by Simon Newcomb, Superin- 
tendent American Nautical Almanac ; formerly Professor at the U. S. 
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charge of survey of the 40th Paral.el. 

Physics. By 

Political Economy. By Francis A. Walker, Ph.D., Professor in 
Yale College. 

Zoology of the Invertebrate Animals. By Alex. Macalister, 
M.D., Professor of Zoology and Comparative Anatomy in the University 
of Dublin. Specially revised ior America by A. S. Packard, Jr., 
M D., Professor of Zoology and Geology in Brown University. 

iKi^NB. — Any books in the series that may be the work of foreign 
authors Will be specially revised for America by some one among the be*t 
American authorities. 



HANDBOOKS for Students and General Re ado 



ASTRON OM Y 



■ BY 

R? S. BALL, LL.D., F.R.S. 

Astronomer Royal for Ireland 



Specially Revised for America 
BY 

SIMON NEWCOMB, LL.D. 

Superintendent American Nautical Almanac, formerly 
Professor at the U. S. Naval Observatory 







NEW YORK 
HENRY HOLT AND COMPANY 

1878 



fit 

7,1* 



Copyright, 1878, 

BY 

HENRY HOLT & CO. 



PRINTED BY TROW'S PRINTING AND BOOKBINDING CO., NEW YORK. 



EXPLANATORY. 



This Series is intended to meet the requirement of 
brief text-books both for schools and for adult readers 
who wish to review or expand their knowledge. 

The grade of the books is intermediate between the 
so-called "primers" and the larger works professing 
to present quite detailed views of the respective sub- 
jects. 

Such a notion as a person beyond childhood re- 
quires of some subjects, it is difficult and perhaps 
impossible to convey in one such volume. Therefore, 
occasionally a volume is given to each of the main 
departments into which a subject naturally falls — for 
instance, a volume to the Zoology of the vertebrates, 
and one to that of the invertebrates. While this ar- 
rangement supplies a compendious treatment for those 
who wish, it will also sometimes enable the reader 
interested in only a portion of the field covered by a 
science, to study the part he is interested in, without 
getting a book covering the whole. 

Care is taken to bring out whatever educational 
value may be extracted from each subject without im- 



vl Explanatory. 

peding the exposition of it. In the books on the 
sciences, not only are acquired results stated, but as 
full explanation as possible is given of the methods of 
inquiry and reasoning by which these results have 
been obtained. Consequently, although the treatment 
of each subject is strictly elementary, the fundamental 
facts are stated and discussed with the fulness needed 
to place their scientific significance in a clear light, 
and to show the relation in which they stand to the 
general conclusions of science. 

Care is also taken that each book admitted to the 
series shall either be the work of a recognized author- 
ity, or bear the unqualified approval of such. As far 
as practicable, authors are selected who combine 
knowledge of their subjects with experience in teach- 
ing them. 



AUTHOR'S PREFACE. 






The present volume is intended for the use of those 
pupils of the higher classes in schools, who, having 
some elementary knowledge of Mathematics, desire to 
gain some information about Astronomy. 

In selecting the subjects which are treated of in 
this volume, much pains has been taken to direct the 
attention of the reader to the fundamental principles 
of the science. It has, therefore, been necessary to 
suppress many descriptive details which, however in- 
teresting, are not essential to the object in view. 

ROBERT S. BALL. 



Observatory, Duns ink, Co. Dublin : 
September I, 1877. 



CONTENTS. 



CHAPTER I. 

INTRODUCTION. 

PAGB 

The Measurement of Angles — Measurement of an Angle in 
Circular Measure — The Sphere . .... I 

CHAPTER II. 

THE APPARENT DIURNAL MOTION OF THE 

HEAVENS. 

Explanation of Terms - Stars and Constellations — The Pole 
Star — The Great Bear —The Pleiades — The Equatorial 
Telescope— The Clock Movement— The Celestial Globe 7 

CHAPTER III. 

THE FIGURE OF THE EARTH, 

The Earth a Sphere— Figure of the Earth ... 15 

CHAPTER IV. 

THE ROTATION OF THE EARTH ON ITS AXIS. 

Rotation of the Earth— Shape of the Earth connected with 
the Diurnal Rotation 1 7 



Contents. 



CHAPTER V. 

RIGHT ASCENSION AND DECLINATION. 

PAGE 

Introduction— The Transit Instrument — Adjustment of the 
Transit Instrument — Error of Collimation — Error of 
Level — Error of Azimuth— The Astronomical Clock — 
Determination of Right Ascensions — Declination — Lati- 
tude — Phenomena dependent on Change of Place — The 
Meridian Circle — Observation of the Nadir— Refraction 
— Calculation of Refractions — Latitude . . . 19 



CHAPTER VI. 

THE APPARENT MOTION OF THE SUN. 

The Sun appears to move among the Stars — Observation 
of the Pleiades -The Ecliptic . . . . . 42 

CHAPTER VII. 

SIDEREAL TIME. 
Sidereal Day — Setting a Sidereal Clock . • • .46 

CHAPTER VIII. 

MEAN TIME. 

Mean Time — Apparent Solar Day — The Mean Sun — De- 
termination of Mean Time — -The Mean Solar Day — 
Determination of the Sidereal Time at Mean Noon- 
Determination of Mean Time from Sidereal Time — De- 
termination of Mean Time at a given Longitude— The 
Year 51 



Contents. xi 

CHAPTER IX. 

THE PLANETS. 

PACK 

Meaning of the word Planet — Motion of the Planet Venus 
— Apparent Motion of the Planet Mercury — The Earth 
is really a Planet— The Earth's Orbit is nearly Circular 
— The Orbit of Venus — Telescopic appearance of Venus 
explained — Effect of the Annual Motion of the Earth on 
the Appearance of Venus — The Orbit of Mercury — The 
Apparent Motions of Mars ...... 59 

CHAPTER X. 

KEPLER'S LAWS. 

Orbits of the Planets are not Perfect Circles— Kepler's first 
Law — Kepler's second Law— Kepler's third Law . • 7 1 

CHAPTER XI. 

THE LAW OF GRAVITATION. 

Gravitation of the Earth - Gravitation towards the Sun — 
Illustration — Explanation of the Motion of a Planet in a 
Circular Orbit -<-Moticn of a Planet in an Ellipse — Motion 
of Comets 75 

CHAPTER XII. 

PARALLAX. 

Distance of the Moon from the Earth — Distance of the Sun 
from the Earth — The Transit of Venus . . . .82 



PAGH 



X ii Contents. 



CHAPTER XIII. 

PARALLAX OF THE FIXED STARS. 

The Fixed Stars— Annual Parallax of a Star— Determina- 
tion of the Difference of the Parallax of two Stars— The 
Proper Motion of the Stars— Distance of the Stars . 9° 



CHAPTER XIV. 
THE PRECESSION OF THE EQUINOXES. 

Alterations in the Right Ascensions of Stars— Precession of 
the Equinoxes— The Ecliptic is at Rest— Motion of the 
Celestial Pole— The Obliquity of the Ecliptic— Motion 
of the Pole among the Stars —The Pole of the Earth- 
Permanency of an Axis of Rotation— Cause of the Pre- 
cession of the Equinoxes— Illustration of the Pegtop— 
Precession due to both Sun and Moon . . . .96 



CHAPTER XV. 

THE ABERRATION OF LIGHT. 

The Aberration of Light— Explanation of the Aberration 
of Light— Determination of the Velocity of Light— Other 
Determinations of the Velocity of Light . . .107 



CHAPTER XVI. 

THE SEASONS. 
Changes of the Seasons II2 



Contents. xiii 

CHAPTER XVII. 

THE SOLAR SYSTEM. 

PAGB 

The Solar System— The Planets u6 

CHAPTER XVIII. 

THE FIXED STARS. 

Magnitudes of the Stars — Numbers of the Stars— The 
Milky Way — Clusters of Stars — Globular Clusters- Tele- 
scopic Appearance of a Star — Variable Stars — Proper 
Motion of Stars — Motion of the Sun through Space — 
Real proper Motion of the Stars— Double Stars— Castor 
as a Binary Star —Motion of a Binary Star — Dimensions 
of the Orbit of a Binary Star — Determination of the Mass 
of a Binary Star — Colours of Double Stars . • .120 

CHAPTER XIX. 

NEBULAE. 

Nebulae — Classification of Nebulas • • • • • 142 

CHAPTER XX. 

SPECTRUM ANALYSIS. 

Composition of Light — Construction of the Spectroscope . 146 



ASTRONOMY. 



CHAPTER I. 

INTRODUCTION. 

§ i. The Measurement of Angles. — We assume 
that the pupil, before he begins to learn astronomy, 
knows at least as much geometry as is contained 
in the first three books of Euclid. It will also be 
greatly to his advantage to have some acquaintance 
with trigonometry ; but this will not be indispensable 
for the reading of this volume, which is only an intro- 
duction to the science. 

If a right angle be divided into ninety equal parts, 
each one of the parts thus obtained is termed a degree. 
If a degree be subdivided into sixty equal parts, each 
one of these parts is termed a minute] and if a minute 
be subdivided into sixty equal parts, each one of these 
parts is termed a second. 

An angle is therefore to be expressed in degrees, 
minutes, and seconds, and, if necessary, decimal parts 
of one second. For brevity certain symbols are used : 
thus 49 13' ii"'4 signifies 49 degrees, 13 minutes, 11 
seconds, and four-tenths of one second. 

B 



2 Astronomy. 

We shall now explain what is meant by a graduated 
circle. Let the circumference of a circle adb (fig. i) 
be divided into 360 parts of equal length. The divi- 
sion lines separating these parts are denoted by o°, 
i°, 2 , &c., up to 359°. It is usual to engrave upon 
the circle only those figures which are appropriate 
to every tenth division. The actual numbers found 
on the circle are therefore o°, io°, 20 , &c. (fig. 1). 

Fig. i. 




270° 



There is, however, no difficulty in finding at a glance 
the number appropriate to any intermediate division. 
To facilitate this operation the divisions 5°, 15 , 25 , 
which are situated half-way between each of the num- 
bered divisions, are sometimes marked with a longer 
line, so that they can be instantly recognised. 

The interval between two consecutive divisions on 
a circle is often, for convenience, termed a degree. The 
reader must, however, carefully remember that the word 
degree means an angle, and not an arc ; with this cau- 



The Measurement of A ngles. 3 

tion, however, no confusion will arise from the occa- 
sional use of the word to denote the small arc of the 
circle instead of the angle which this arc subtends 
at the centre. 

For the more refined purposes of science, the sub- 
division of the circle must be carried much farther 
than the division into degrees. The extent of the 
subdivision of each arc of one degree into smaller 
arcs depends upon the particular purpose for which 
the graduated circle is intended. 

■ The most familiar instance of a graduated circle is 
the ordinary drawing instrument termed a protractor. 
The protractor is employed for drawing angles of a 
specified size. For example, suppose that from a 
point c in the line a b it is required to draw a line 
cd so that the angle bcd shall be equal to 43 . The 
centre of the protractor is to be placed at c, and the 
division marked o° upon the protractor is to be placed 
upon the line a b ; then a dot is to be placed on the 
paper at the division 43 , and a line drawn through the 
dot from the point c is the line c d which is required. 

The extent of the subdivisions is limited by the 
size of the instrument; thus in a protractor of 20 
centimetres in diameter the length of the arc of one 
degree is 1745 millimetres. If this distance be bi- 
sected, the interval between two consecutive divisions 
is less than one millimetre ; if any further subdivision 
be attempted, the divisions are so close together that 
they cannot be conveniently read without a magnifier : 
a protractor of this size is therefore usually only 
divided to 30-minute spaces. 

For astronomical instruments the graduated circles 
b 2 



4 Astronomy. 

are generally divided to a greater extent. In the 
instrument known as the meridian circle, the divisions 
of the circles are executed on silver, and two consecu- 
tive divisions are sometimes only two minutes apart. 
Thus the entire circumference contains 30 x 360 = 
10800 divisions. The circles in this case are nearly 
a metre in diameter, and the divisions are read by 
microscopes. 

Mechanical ingenuity has, however, obviated the 
necessity for carrying the subdivisions of the arc to an 
inconvenient extent. In the best circles we are now 
able to ' read off/ as it is termed, to the tenth part of 
one second. If this were to be effected by divisions 
alone, there would have to be 12,960,000 distinct 
marks upon the circumference, and this is clearly im- 
possible with circles of moderate dimensions. Into the 
details of these contrivances it is unnecessary to enter. 

§ 2. Measurement of an Angle in Circular Mea- 
sure. — There is another method of measuring angles, 
which, though unsuited for the graduation of astrono- 
mical instruments, is still of the greatest importance in 
many astronomical calculations. If we measure upon 
the circumference of a circle an arc of which the 
length is equal to the radius of the circle, and if we 
join the extremities of this arc to the centre, the join- 
ing lines include a definite angle, which is termed 
the unit of circular measure, or the radian. It will 
easily be seen that the angle of the radian is the same, 
whatever be the size of the circle. 

We can now see how the magnitude of any given 
angle may be expressed by the number of radians and 
fractional parts of one radian to which the given angle 



Measurement in Circular Measure. 5 

is equivalent, and this number is called the circular 
measure of the given angle. It is often necessary to 
convert the expression for the magnitude of an angle 
in radians to the equivalent expression in degrees ; 
minutes, and seconds. To accomplish this we first cal- 
culate the number of seconds in one radian. 

Since the circumference of a circle is very nearly 
equal to 3*14159 times its diameter, the arc of a semi- 
circle may be taken as equal to 3*14159 radii. Hence 
the angle subtended at the centre by the semicircle must 
be equal to 3*14159 radians, and hence it appears that 
3*14159 radians must be equal to 180 degrees, whence 
by division it will be found that one radian is equal to 
206265 seconds very nearly. We have often in astro- 
nomy to make use of the assumption that the length 
of a very small arc of a circle is practically equal to 
the length of the chord of the same arc. Perhaps 
there is no simpler way of justifying such an assump- 
tion than by actually exhibiting the difference in a par- 
ticular case. If a circle be drawn with a diameter of 
one metre, and if an arc one centimetre in length be 
marked on its circumference, then the length of the 
chord of that arc is 0*99996 centimetres : so that the 
arc is only one twenty-five thousandth part longer than 
the chord. It is obvious that the difference between 
the length of the chord and the length of the arc in 
such a case as this may for all ordinary purposes be 
neglected. 

To illustrate the application of this principle we 
shall state here a problem which very often occurs in 
astronomy. A distant object a b (fig. 2) subtends an 
angle 0" at o, the distance o a being equal to d. It is 



Astronomy. 



required to determine the length a b. If a circle be 
described around o as centre to pass through the points 
A and b, the length of the chord a b may practically be 

considered to be equal to 

Fig. 2. . «r i 

the arc a b. We may, there- 
fore, compute the arc in- 
stead of the chord. Now, 
since the angles subtended 
by arcs are proportional to 
the lengths of those arcs, it follows that the required 
distance ab must bear to the angle 0", subtended by 
it at o, the same proportion that the radius d bears to 
or 






the angle 206265 



AB = 



-. d. 



206265 

§ 3. The Sphere. — A sphered a surface such that 
every point upon it is equidistant from one point in 
the interior, which is called the centre. If a plane be 
drawn through the centre of the sphere, it cuts the 
sphere in a circle, which is called a great circle. A 
plane which cuts the sphere, but which does not pass 
through the centre, has also a circle for the line along 
which it intersects the sphere ; this is called a small 
circle. The radius of a great circle is of course equal 
to the radius of the sphere. The radius of a small 
circle may be of any length less than the radius of the 
sphere. We may suppose that a sphere is produced 
by the revolution of a circle about its diameter, and 
the radius of the sphere is then equal to the radius of 
the circle from which it has been produced. 

Let o be the centre of a sphere and a and b any 



The Sphere. 7 

two points on its surface. Then a plane through the 
three points o a b cuts the sphere in a great circle. 
This may, for simplicity, be termed the great circle 
a b. The length of the arc of the great circle con- 
necting two given points on a sphere of known radius 
is most conveniently measured by the angle which 
the arc subtends at the centre. 

If three points a b c be taken upon the surface of 
a sphere, then the three great circles a b, b c, a c 
form what is called a spherical triangle. The sides of 
this triangle are measured by the angles which they 
subtend at the centre. The spherical triangle has 
also angles at its three vertices abc; the angle at 
a, for example, is the angle contained between the two 
planes oab and o a c. Thus the six quantities in- 
volved in the consideration of a spherical triangle are 
all angular magnitudes. 

The three angles of a plane triangle are together 
equal to two right angles, but in the spherical triangle 
the sum of the three angles always exceeds two right 
angles. 



CHAPTER II. 

THE APPARENT DIURNAL MOTION OF THE HEAVENS. 

§ 4. Explanation of Terms. — To an observer sta- 
tioned in the middle of a plain where his view is not 
obscured in any way by mountains or other obstruc- 
tions, or, better still, to an observer stationed on a 
vessel at sea and out of sight of land, the heavens 



8 Astronomy. 

appear like a hemispherical vault with a circular base 
resting upon the earth. This circular base, which 
seems like the intersection of the heavens with the 
earth, is termed the apparent horizon. 

If a weight be suspended by a thread from a fixed 
point, then, when the weight is at rest, the thread is 
said to be vertical. That point of the heavens to which 
the thread points, and which it would appear to reach 
if it could be prolonged indefinitely upwards, is called 
the zenith \ while, if the direction of the thread were 
prolonged downwards through the earth, it would 
intersect that portion of the celestial vault which is 
below the horizon in a point called the nadir. 

A straight line which is perpendicular to a vertical 
line is called a horizontal line ; and all the straight 
lines which can be drawn perpendicular to a vertical 
line through any one point in it lie in one and the 
same plane, which is called a horizontal plane. 

If the face of an observer (in the northern hemi- 
sphere) be directed towards that part of the heavens 
where the sun is at noon, the part of the heavens in 
front of him is termed the south, that behind him is 
the north, while the east is on his left hand and the 
west upon his right. 

§ 5. Stars and Constellations.— To learn anything 
of astronomy thoroughly it is absolutely essential for 
the beginner to obtain a knowledge of some of the 
principal stars and constellations, so that he may be 
able to recognise them and observe for himself the 
apparent motions now to be described. For this pur- 
pose he must have the use either of a celestial globe 
or of a good set of celestial maps. The beginner will 



Stars and Constellations. 



Fjc. 3- 



be saved much time if his teacher can actually show 
him on the heavens the principal constellations and 
impress their names and appearances on his memory. 

To make the coarse observations which will be 
described to begin with, no telescope or other instru- 
ments are required. The following are the objects to 
which the learner should first direct his attention. 

§ 6. The Pole Star. — This star can be seen on 
every clear night. To identify the Pole, it is ne- 
cessary for the learner to know 
the constellation of the Great 
Bear, sometimes called the 
Plough (rig. 3). The two stars 
a and b are commonly called 
the pointers, for they point 
nearly up to the Pole Star p. 
The first thing to be observed 
about the Pole Star is that 
it remains constantly in the 
same position in the heavens. 
At different hours of the night 
or at different seasons of the 
year the Pole Star will con- 
stantly be seen in the north at about the same elevation 
above the horizon. It is true that with more careful 
observations this statement would be found to be not 
literally accurate, for the Pole Star does really change its 
position to a small amount. 

§ 7. The Great Bear. — The student will next ob- 
serve the Great Bear. He is carefully to note the 
position of the seven stars at an early hour in the 
evening, and if he then looks at them again a few 




IO Astronomy. 

hours later he will see a remarkable change. The 
relative positions of the seven stars have not changed 
inter se — the shape of the constellation is not altered — 
but the whole group has moved bodily in the heavens. 
He will still see the two pointers directed towards the 
Pole Star, which has remained where it was; and thus 
the idea will be suggested to him that the whole con- 
stellation has moved as if all the seven stars were fas- 
tened together with invisible rods, and as if each of 
the seven stars were fastened by an invisible rod to the 
Pole Star. If he continued his observations for the 
whole of the night and the following day (as he could 
do if he had a suitable telescope), he would find that 
the Great Bear, after ascending from the east, passed 
over the observer's head, then down towards the west 
under the Pole Star in the north, and round again to 
the east ; and he would find that in a trifle less than 
twenty-four hours the constellation had returned 
exactly to its original position. 

§ 8. The Pleiades. — This is a beautiful cluster of 
stars in the constellation of the Bull, and somewhat 
resembles a miniature of the Great Bear. This well- 
known group is visible at night throughout the greater 
part of the year, but it need not be looked for from 
the middle of April to the middle of June. Winter 
is the best season for observing it. In November it 
will be seen in the east shortly after sunset ; it will 
then gradually rise until about midnight, when it 
reaches its greatest height ; it will then gradually 
descend towards the west, where it will disappear. 
There is, however, a very great difference between the 
motion of the Pleiades and that of the Great Bear : 



Pleiades. 1 1 

the latter could be followed (with a telescope) through- 
out its complete revolution; but this is not so with 
the Pleiades, for they actually go below the horizon 
on the west and come up again on the east. If, how- 
ever, the time be noted which elapses between two 
consecutive returns of the Pleiades to the same posi- 
tion, the interval will be found equal to the time of 
revolution of the Great Bear. It will also be observed 
that the Pleiades appear to turn round the Pole Star 
in the same manner as the Great Bear. 

§ 9. The Equatorial Telescope. — The motion 
which we have been describing is called the ap- 
parent diumal motion of the heavenly bodies. To 
study this motion with the accuracy which its import- 
ance demands we employ the very important astrono- 
mical instrument which is called the equatorial tele- 
scope. For an account of the optical construction of 
the telescope we must refer to books upon Optics ; 
we are now merely going to describe the manner in 
which the equatorial telescope is mounted. 

The equatorial consists of a telescope p q (fig. 4) 
attached at its centre o to an axis a b, called the polar 
axis ; the telescope is capable of being turned round 
the axis passing through o, while the polar axis is 
capable of being turned round the pivots at a and b. 
By the combination of these two motions it is possible 
to direct the telescope towards any required point. 
To adjust the instrument, it is necessary to place the 
polar axis a b so that its direction if continued would 
intersect the heavens in a particular point very close to 
the Pole Star. This point is called the Pole. Let us 
now suppose that the telescope P Q is pointed towards 



1 2 Astronomy. 

a star shortly after it has risen, and that the telescope 
is then < clamped,' so that it can no longer turn 
around the axis through o, but so that the motion 
of the polar axis round a b is not interfered with. 
It will then be found that, by simply turning the 
polar axis slowly round, the star can be kept in the 
field of view, although the angle boq remains unal- 
tered. If the telescope be turned to any other star, 
the angle boq must first be altered until the star is 

brought into the field 
of view ; then the tele- 
scope is clamped again, 
and the star may be fol- 
lowed by simply turning 
round the polar axis. If 
we turn the instrument 
to the Pole Star itself, 
we shall now see what 
the coarser observation 
failed to indicate — namely, that the Pole Star is itself 
in motion. In this case the angle b o Q is extremely 
small, being about i° 20'. 

If the polar axis of the equatorial be not pointed 
exactly to the correct point of the heavens, it will not 
be found that a star can be followed from its rising 
to its setting without altering the angle boq. There is 
only one point visible in this hemisphere to which the 
polar axis can be directed so as to fulfil this condi- 
tion. In the southern hemisphere there is of course 
a corresponding point, called the South Pole. 

Let p denote the Pole (fig. 5), e p the direction of 
the polar axis, and e s the direction of the telescope 




The Equatorial Telescope, 1 3 

when pointed to a certain star. Then the apparent 
motion of the star is such that the angle sep remains 
constant. Now, since the arc P s is proportional to 
the angle p e s, it follows that the arc p s remains con- 
stant, and that therefore the arcs p s, p l, p m, p n, 
drawn from the Pole to different parts of the star's appa- 
rent path, must be all equal. Hence we learn the very 
important result that the apparent motions of the stars 
are in small circles on the surface of the heavens, and 
that all these small circles have 

, r , . , Fig. 5. 

the same point for their pole. 

§ 10. The Clock Move- 
ment. — It having been ascer- 
tained by the equatorial that 
all the stars appear to move 
in small circles, the next 
question to be considered is 
the rate at which the move- 
ment of each star is effected. 
It is found that to follow the 

star the polar axis of the equatorial is to be turned 
round with perfect uniformity. In fact, a clock-work 
arrangement is generally adapted to the equatorial, 
which turns the polar axis round with a perfectly 
equable motion, and as the star is then seen to remain 
constantly in the field of the telescope, it follows that 
the star moves with uniformity in its apparent path. 

Suppose now the clock be adjusted to move the 
polar axis of the equatorial telescope accurately for 
one star, and that then the telescope be directed to 
another star ; it will be found that the telescope will 
likewise follow the second star with perfect regularity. 




14 Astronomy. 

From this, the very important result follows that the 
time occupied in the apparent diurnal motion is the 
same for every star. 

We may summarise the results at which we have 
arrived in the following way : — 

(i) All the stars appear to move in circles round a 
point of the heavens called the Pole. 

(2) Each star moves uniformly in its circle. 

(3) The time occupied by each star in completing 
its motion is the same and is equal to 23 h. 56 min. 4 sec. 

§ n. The Celestial Globe. — If we imagine the 
angle of a pair of compasses to be placed at the eye, 
while each leg of the compasses is directed towards 
a particular star, the angle between the legs of the 
compasses is said to be the angular distance between 
the two stars. By an instrument founded on this 
principle it is possible to measure the angular distance 
between two stars with great accuracy, and from such 
measurements a celestial globe can be constructed. 
Two stars, a and b, suppose, are first to be set down at 
the proper distance apart \ then the distance of a third 
star s is to be measured from both a and b, and the star 
s is to be marked upon the globe so that the two arcs, 
s a and s b, shall subtend at the centre of the globe 
the angles which have been observed. In this way 
all the principal stars can be marked down on the 
globe. Now, it is exceedingly remarkable that, not- 
withstanding the incessant diurnal motion, the posi- 
tions of the stars with respect to one another remain 
constant for centuries. 

The catalogue of Ptolemy enables us to draw the 
stars of the Great Bear as that constellation was seen 



The Celestial Globe. 15 

nearly 2,000 years ago, and the differences between 
the drawing and the present appearance of the Great 
Bear are so slight that they may perhaps be entirely 
due to the errors which Ptolemy made. 

We have spoken of the motion of the stars as ap- 
parent, and we have now to explain how we know that 
the motion is only apparent, and to show to what the 
apparent motion is really due. To do this we must 
first consider the figure of the earth. 

We shall now introduce a convention which is 
very useful. The stars are no doubt at very varied 
distances from the earth, but, nevertheless, we have 
seen that the appearance of the heavens can be ade- 
quately represented on a globe where all the stars are 
at the same distance from the centre. Let us now 
suppose a colossal globe to be described with the 
earth at its centre and an enormously great radius. 
Then, if the stars were all bright points stuck on the 
interior of this globe, the appearance of the heavens 
would not be altered. This imaginary globe we call 
the celestial sphere. 



CHAPTER III. 

THE FIGURE OF THE EARTH. 

§ 1 2. The Earth a Sphere.— To an observer situated 
upon the surface of the earth the contrast is very wide 
indeed between the appearance of the earth and the 
appearances presented by the sun and moon. The 



1 6 Astronomy. 

earth appears to be a flat plain, more or less diversi- 
fied ; the sun and moon appear to be globular ; the 
earth appears to be at rest, while the sun and moon 
are apparently in constant motion ; and, lastly, the 
earth appears to have a bulk incomparably greater 
than that of either the sun or the moon. 

If, however, we could change oitr point of view to a 
suitable position in space, we should form a more just 
conception of the relation of the earth to the sun and 
moon. We would then see that each of the three 
bodies was really spherical, that each of them was 
really in motion, and that the earth, though larger 
than the moon, was very much less than the sun. 

It is not an easy matter to determine accurately 
the form and dimensions of the earth. The shape of 
the earth is never actually seen except during an 
eclipse of the moon ; the shadow thrown by the earth 
is then seen on the moon ; and as the edge of this 
shadow is always a portion of a circle, we may infer 
that the earth, which forms the shadow, must be 
spherical. 

§ 13. Figure of the Earth. — We must first under- 
stand clearly what is meant by the figure of the earth. 
Suppose that all the large tracts of land on the surface 
of the earth were intersected by numerous canals 
which communicated with the sea. Suppose that the 
sea was perfectly calm and uninfluenced by the tides. 
Conceive that the dry land was now pared away down 
to the level of the canals and the sea; then the figure 
which would be produced by these operations is called 
the figure of the earth. 

It has been found by very careful measurement 



Rotation of the Earth. 



17 



that the figure of the earth is such as would be pro- 
duced by the revolution of the curve called an ellipse 
about its minor axis. In the case of the earth, the 
length of the axis a b (fig. 
6) of the ellipse is 12,712 
kilometres, while the axis 
cd is 12,757 kilometres. 
It will thus be seen that 
the earth does not diifer 
very much from a sphere of 
which the radius is 6,370 
kilometres (=3,958 miles). 
We do not at present enter into the details of the 
measurements by which these results have been ob- 
tained. 




CHAPTER IV. 

THE ROTATION OF THE EARTH ON ITS AXIS. 



§ 14. Rotation of the Earth. — We now revert to 
the subject of the apparent diurnal motion of the 
heavens round the earth. This motion may be ex- 
plained either by the supposition that there is real 
motion of all the stars, with the sun, moon, and 
planets, round the earth from east to west once every 
day, or by the supposition that the earth turns round 
from west to east, and thus produces the apparent 
motion. 

Which of these two solutions are we to adopt? 
c 



1 8 Astronomy. 

We shall see hereafter that many of the celestial 
bodies are vastly larger than the earth, that they are 
situated at very great distances from the earth, and 
that some of these distances are very much greater 
than others. It therefore seems much more reason- 
able to suppose that the earth, which is a compara- 
tively small body, should be in a condition of rotation, 
rather than that the vast fabric of the universe should 
all be moving round the earth once every day. Astro- 
nomers, therefore, now universally admit that the 
earth really does turn an its axis once every 23 11 
5 6 ra 4 s . 

§ 15. Shape of the Earth connected with the 
Diurnal Rotation. — A remarkable confirmation of 
this conclusion is presented by the shape of the earth 
itself. We have already explained what is meant by 
the pole of the heavens (§ 10), and we can conceive a 
straight line drawn from the centre of the earth to- 
wards the north pole of the heavens. This straight 
line will cut the surface of the earth in a point which 
is called the north pole of the earth. Now by means 
of the surveying operations which have determined the 
figure of the earth, we are enabled to ascertain the 
point on the earth's surface which is the extremity of 
the shorter axis of the ellipse by the rotation of which 
the figure of the earth can be produced. It will be 
noticed that the apparent diurnal motion has nothing 
whatever to do with the surveying operations, so that 
it is exceedingly remarkable to find that the north 
pole of the earth is exceedingly close to, if not actu- 
ally identical with, the extremity of the shorter axis of 
the ellipse. Thus we see that the axis about which 



Right Ascension and Declination. 19 

the earth actually rotates coincides with the shortest 
diameter of the earth. 

In this we have another very remarkable proof of 
the reality of the earth's rotation, for suppose the earth 
to have been originally in a fluid or semifluid condi- 
tion, then the effect of the centrifugal force would 
make it bulge out at the equator and flatten it down 
at the poles, and thus impart to it an ellipsoidal shape, 
and the shortest axis of the ellipsoid would coincide 
with the axis of rotation. We are thus led to the 
belief that the observed coincidence between the axis 
of the apparent diurnal rotation of the heavens and the 
shortest axis of the earth is a proof that the apparent 
diurnal motion is really due to the rotation of the earth. 



CHAPTER V. 

RIGHT ASCENSION AND DECLINATION. 

§ 16. Intro ductioi). — We now proceed to consider 
how the positions of the stars and other celestial bodies 
on the surface of the heavens may be determined. 
We are not now speaking of the actual position of a 
celestial body in space. To know such a position 
we should require to know the distance of the body 
from the earth, and of this in the great majority of cases 
we are at present entirely ignorant. What we desire 
to ascertain now is the apparent place upon the sur- 



20 



Astronomy. 



Fig. 7. 



face of the heavens, so that we may know exactly 
where to look for the object, or, to speak more strictly, 
that we may be able to point a telescope so as to be 
sure of finding the object at once. It will be under- 
stood that we are not now speaking of the position of 
the object with reference to the horizon, which, of 
course, is changing every hour, but of its position 
with reference to the stars and constellations. 

§ 17. The Transit Instrument. — It will be conve- 
nient at this point to give a description of one of the 
most important instruments in an astronomical observa- 
tory. The essential principles of the transit instru- 
ment may be explained by 
help of fig. 7. An ordinary 
telescope, a b, is fixed to 
an axis at right angles to 
the telescope. The shape 
of the axis and the method 
of attachment of the tele- 
scope thereto, are spe- 
cially designed so as to 
secure as much rigidity as 
possible. At the extremi- 
ties of the axis are pivots, 
x y, which turn in suitable fixed bearings supported 
on solid masonry piers. Thus the transit instrument 
can be moved in one plane only. In the focus of the 
telescope, close to the eye-piece at a, are stretched a 
number of fine lines, usually spiders' webs ; these are 
placed at equal distances apart, and perpendicular to 
the axis about which the telescope revolves. 

When the telescope is pointed to a star, the image 




The Transit Instrument. 



21 



of the star is formed in the same plane as the spider's 
lines, and as the star moves by the diurnal motion 
the image of the star is seen to pass across each of 
the lines in succession. The central line a b (fig. 8) 
passes through the optical axis of the telescope. In 
addition to the vertical lines, there is a horizontal line 
c d which is parallel to the axis about which the tele- 
scope revolves. The imaginary line joining the point 
of intersection o to the centre of the object glass of 
the telescope is called the axis of collimation. 

The pivots are cylindrical, and the axes of these 
two cylinders are in the same straight line with the 
axis about which the tele- 
scope rotates. 

§ 1 8. Adjustment of the 
Transit Instrument. — We 
shall now explain the condi- 
tions which must be fulfilled 
in order that the transit in- 
strument may be properly 
adjusted. In the first place 
the line of collimation of 
the telescope must be at 
right angles to the axis of the pivots. Now, although 
the instrument-maker can effect this to a high degree 
of approximation, yet the excessive delicacy of astro- 
nomical observation is such that minute errors, which 
entirely elude detection by ordinary measurement, 
become significant under the high magnifying powers 
with which the telescope is armed. We therefore 
require methods not so much for ascertaining whether 
each adjustment of the instrument is correct, as for 




22 Astronomy. 

measuring how far each one is incorrect, and then 
correcting every observation for the irregularity. For 
the present, however, it will be sufficient to point out 
the means whereby the instrumental errors (as they 
are called) can be detected. 

§ 19. Error of Collimation.— Let a b (fig. 9) be 

the axis of the pivots and x y the axis of collimation, 

and let the telescope be directed so that a distant mark 

p is on the axis of collimation ; when this is the case 

the mark is seen in the telescope to coincide with o 

FlG the intersection of the cen- 

•p tral vertical wire with the 

\ horizontal wire (fig. 8). Now, 

suppose the telescope to be 

; x lifted out of its bearings and 

' replaced with the pivots re- 

B versed — i.e., the pivot which 

was formerly to the east is 
\ now at the west — and let the 

\y telescope be again directed 

to the distant mark, then if 
the axis of collimation be not at right angles to the axis 
of the pivots the telescope will now occupy the position 
of the dotted line x'y' and the object p will no longer 
be seen at the point o of the wires. The error of col- 
limation is then equal to half the angle xcx'. To 
correct this error the frame containing the set of wires 
is to be moved until it is found that a distant object 
which coincides with o when the telescope is in one 
position also coincides with o when the telescope is 
in the reversed position. 

When the collimation has been adjusted, if the 



The Transit Instrument. 23 

telescope be turned round the axis of the pivots the 
axis of collimation moves in a plane which traces out 
a great circle on the surface of the heavens. 

§ 20. Error of Level. — The next adjustment of 
the transit instrument consists in placing the axis of 
the pivots horizontal. This is effected by a spirit 
level, which can be hung from the pivots by hooks. 
On the tube of the spirit level a scale is engraved, so 
that the positions of the extremities of the bubble can 
be read off and thus the position of the centre of the 
bubble ascertained. The level is then reversed, so 
that the hook which was formerly on the east pivot is 
now on the west, and vice versa. If the position of 
the bubble be unaltered, then the axis of the pivots is 
horizontal. If the bubble change its position with 
reference to the scale, then the axis of the pivots is 
not horizontal, and one of the pivots must be raised 
or lowered accordingly. 

When the level of the pivots has been pro- 
perly adjusted the great circle which the axis of 
collimation traces out on the celestial sphere will pass 
through the zenith (§4). 

§ 21. Error cf Azimuth. — For the third and last 
adjustment of the transit instrument, we have to 
resort to observations of the heavenly bodies. The 
great circle which the axis of collimation traces out 
must pass through the pole of the heavens as well as 
the zenith of the place of observation, the great 
circle thus defined being called the meridian of the 
place. 

For this adjustment we require the assistance of 
a good clock to enable us to make observations of a 



24 



Astronomy. 



star near the pole, preferably the Pole Star itself. Let 
a c b d (fig. 10) represent the apparent path of the cir- 
cumpolar star around the true pole o. There will be 
but little difficulty in adjusting the transit instrument 
approximately in the true position, so that we may sup- 
pose the vertical circle which the axis of collimation 
describes on the heavens to cut the circle a c b d in the 
points e and f. The final adjustment will consist in 
placing the telescope so that this line e f shall coincide 
with a b. Now, in a period of 23 11 56 111 4 s which is 
often called the sidereal day, the star moves com- 
pletelyxound the small circle. It would therefore as its 

motion is uniform take half 
a sidereal day to move from 
a through c to b. It would, 
however, take more than 
half a sidereal day to move 
from e round by a c and b to 
f, and less than half a sidereal 
day to move from f through 
d up to e. We therefore 
make the following observa- 
tions. We first note the moment by the clock when 
the star passes the middle wire of the transit instrument 
directed to e. About twelve hours afterwards we direct 
the telescope to f and note the time when the star 
passes the same wire, and again twelve hours after we 
repeat the observation at e. Now, if the interval of 
time as measured by the clock between the first and 
second observations is equal to the time between the 
second and the third observations, then the telescope 
is correctly adjusted ; but if these intervals are not 




The Astronomical Clock. 2$ 

equal, then one of the pivots must be moved north or 
south until the adjustment is completed. The three 
adjustments having been made, the transit instrument 
is in working order. 

We shall now describe the method of using the 
transit instrument in the observatory, and its adjunct 
the astronomical clock. The point in which the 
meridian cuts the horizon on the same side of the 
zenith as the pole is the northern point ; thus the 
pivots of the transit instrument when properly adjusted 
point due east and due west, while the points on the 
horizon which can be seen in the transit instrument 
are the north point and the south point. If we could 
imagine the line of the meridian actually drawn upon 
the surface of the heavens we could then see the stars 
crossing this line, and could note the instant by the 
astronomical clock at which each star crossed. Now, 
the central wire of the transit instrument really coin- 
cides with the meridian, and therefore by noting the 
instant when the star passes across the wire we obtain 
the instant when the star crosses the meridian. We 
have, too, the advantage that the telescope renders 
minute stars visible, and by its magnifying power 
enables the coincidence of the star and the wire to be 
observed with great precision. 

§ 22. The Astronomical Clock. — The first thing to 
be done is to make the clock keep accurate sidereal 
time. For this purpose the transit instrument' is to be 
directed to any bright star, and the moment at which 
the star passes the central wire of the instrument 
is to be noted by the clock. The next day the same 
star is to be observed again, and if the clock be going 



26 Astronomy. 

correctly, it will show exactly a difference of twenty- 
four hours between the two observations. It is im- 
material for this purpose what star be chosen ; but it 
is, however, convenient to select a star at a consider- 
able distance from the pole, for then its apparent 
motion is rapid, and the moment of its transit across 
the wire can be observed with accuracy. If the clock 
do not show an interval of exactly twenty-four hours 
between the two observations, then the length of the 
pendulum must be altered by screwing up the bob if the 
clock be too slow, or screwing down the bob if the 
clock be too fast. It will not be possible to make the 
clock go with perfect accuracy, but if the clock be 
going very nearly right, then the amount which it 
gains or loses in twenty-four hours is determined. 
This is called the clock's rate, and the test of a good 
clock is that the rate should remain uniform. 

When the rate is determined, then all the observa- 
tions can be corrected, so that we may suppose for 
present purposes that the clock is going correctly. 
We have now another point in the adjustment of the 
clock to attend to. Suppose that the pendulum is 
adjusted perfectly, and that the hands of the clock 
indicate o h o m o s , and that you wish to start the clock, 
how are you to choose the instant at which to start it? 
There is a certain point in the heavens called the ver- 
nal equinox, the importance of which will be explained 
subsequently (§ 34). Now. if a star were situated ex- 
actly at the vernal equinox, then, when this star was 
seen on the central wire of the transit instrument, the 
clock should be started. Now, although there is no 
star actually situated at the vernal equinox, yet we 






Right Ascension. 27 

know the position of this point so accurately that we 
can proceed as if we could actually observe the transit 
of the vernal equinox, and then at this moment start 
the clock. 

§23. Determination of Right Ascensions. — We 
shall now suppose that both the transit instrument 
and the astronomical clock are in perfect order, and 
we shall describe the use of them in determining the 
positions of stars. The observer having pointed the 
telescope so that the star which he wishes to observe 
shall shortly be brought into the field by the diurnal 
motion, takes his seat at the instrument, and after a 
glance at the clock commences counting the seconds. 
If he be looking towards the south, the star comes in 
at his right hand and approaches the wires. Let x 
be the position (fig. 8) which the star has at one tick 
of the clock, then by the next tick it will have passed 
across the wire and be found at y. The experienced 
observer will rapidly estimate to a fraction of a second 
the instant when the star coincided wiih the wire, and 
he will note this down. Without taking his eye from 
the telescope he repeats this operation for each of the 
five wires, and he takes the mean of the five observa- 
tions for the time of transit over the middle wire. By 
this method he obtains the time of transit more accu- 
rately than he would have done if he had depended 
upon the single observation at the middle wire. 

Let us suppose that the observation of the same 
star was repeated night after night, it would be found 
that the same star always returned to the meridian at 
the same ti??ie (subject only to certain minute differ- 
ences which need not now be considered). The time 



28 



Astronomy. 



at which the star reaches the meridian is called the 



right ascension of the star. 



§ 24. Declination.— Suppose it was desired to give 
instructions to a transit observer to observe a parti- 
cular star, he must in the first instance know the right 
ascension of the star, so that when the astronomical 
clock is getting near that hour he can take his posi- 
tion at the instrument. Suppose, however, the star 
were invisible to the unaided eye, then it is clear that 
the observer must be furnished with instructions as to 
ho7V high the telescope ought to be pointed, as well as with 
reference to the time of transit. When once the time 
is known, and also the height at which the telescope 
is to be pointed, then it is clear that the position of 
the star is completely specified. We have now to 
consider the means which astronomers have adopted 
for specifying this second element of jthe position of a 
heavenly body. 

If through the centre of the earth a plane be drawn 
perpendicular to the line drawn from the centre of the 

earth to the celestial pole, 
this plane cuts the celestial 
sphere in a great circle 
which is called the celestial 
equator. Every point of the 
equator is 90 from the pole. 
Let p (fig. n) represent 
the celestial pole, and atb 
the celestial equator, draw 
from p an arc of a great circle pst passing through 
s, the position of a star upon the surface of the 
heavens. If we join o s and o t, the angle t s is 



Fig. : 




Latitude. 29 

called the declination of the star s. The angle p o s is 
called the polar distance of the star, so that the polar 
distance is the complement of the declination. If the 
star be north of the equator, i.e. between the north 
pole and the equator, then the declination is positive ; 
but if the star be south of the equator, so that its 
polar distance is greater than 90 , then the declination 
is negative. 

The declination of a star and its right ascension 
completely define the position of the star, and they 
are both independent of the spot on the earth on 
which the observer may be situated. We have now 
to explain how the declination is connected with the 
angular elevation at which the telescope should be 
pointed in order to see the star in the centre of the 
field at its moment of transit. 

§ 25. Latitude. — We must first explain what is 
meant by the latitude of a point upon the earth's sur- 
face. Let c (fig. 12) represent the centre of the 
earth, and let R be a point on the earth's surface ; 
through c draw a line c p pointing to the celestial pole, 
then this cuts the surface of the earth in what are 
known as the North and South Poles respectively. 
Through c draw a plane perpendicular to c p, then 
this plane cuts the surface of the earth in a great circle 
which is known as the earth's equator. Join c R, then 
the angle r c h is the latitude of the place R. It will 
be seen at once that the latitude of a point on the 
equator is o°, and that the latitude of the pole is 90 . 

Suppose an observer at r looks towards the celes- 
tial pole, he will see it exactly in the same position 
with reference to the stars as if he were able to see it 



30 



Astronomy. 



Fig. 12. 



from the centre of the earth. The reason of this is, 
that the stars are so enormously distant from the earth 
that a change in the position of the observer on the 
surface of the earth produces only an insensible change 
in the apparent position of the stars. The line r q 

parallel to c p is therefore 
the direction of the celestial 
pole viewed from r. 

The line R a drawn per- 
pendicular to cr (we are 
for the present assuming 
the earth to be spherical) 
denotes the horizon, so 
that the angle Q r a ex- 
presses what is called the 
elevation of the pole above 
the horizon. Now since 
a r c is a right angle, it 
follows that Q R a and hrc 
must together make up a 
right angle, and since rhc 
is a right angle, it follows that hrc and h c r must 
together make up a right angle, whence taking away 
H r c in both cases, it follows, that qra must be equal 
to rch. Hence we have the very important pro- 
position which is thus stated : — 

The elevation of the pole above the horizon is equal 
the latitude of the place. 

§ 26. Phenomena dependent on change of Place. 
This proposition will explain the very remarkable 
changes in the appearance of the heavens which are 
presented to a traveller who makes a considerable 




Culmination. 3 1 

change in his latitude. In the north the pole appears 
high up in the heavens, in fact at the north pole of 
the earth the celestial pole would be at the zenith. 
As the traveller proceeds towards the south, the pole 
gradually sinks, until when he is on the equator the 
pole will be in his horizon. At the equator all the 
stars will be seen to rise perpendicularly, and every 
star will continue above the horizon for half a sidereal 
day. The observer at the pole will only see half the 
heavens, as the equator constitutes his horizon, and 
all objects below the equator will be invisible to him ; 
all the stars in the northern hemisphere will, however, 
be to him circumpolar stars > that is, stars which never 
set. The observer at the equator will, however, be 
able to see every star in the heavens, but he will have 
no circumpolar stars. 

We shall now consider more fully the condition 
under which a star is visible at a given latitude. The 
meridian of a place extends right round the celes- 
tial sphere, consequently by the diurnal rotation of 
the heavens every star crosses the meridian twice each 
sidereal day. When a star reaches the meridian it is 
said to culminate, and the culmination which takes 
place above the pole is called the upper culmination, 
and that which takes place below the pole is the lower 
culmination. We have to consider when the star is 
visible at one or both of its culminations. Since the 
elevation of the pole is equal to the latitude of the 
place, it follows that the angular distance of the 
zenith and the pole is equal to the complement of 
the latitude of the place, or to what is called the co- 
latitude (§ 28). 



32 



Astronomy. 



In fig. 13 let p denote the pole, z the zenith, and 
s, s' the positions of a star at upper and lower culmi- 
nations respectively. Let </> be the latitude and the 
declination of the star. 

Then the zenith distance of the star at lower cul- 
minate is z s', but 

zs'= zp + ps' 

= 90 -^ + 90 — 2 = 180 — <p — d. 

Now, in order that a star be visible it is necessary 
that its zenith distance be less than 90 . Hence for a 
star to be visible at lower culmination we must have 

180— — 3<9O° 
or c>go — (j). 

Hence if a star be visible at lower culmination its de- 
clination must exceed the colatitude. If a star be 

Fig 13. 




visible at lower culmination it will a fortiori be visible 
at upper culmination. 

Now suppose a southern star at t (fig. 13). Its 
zenith distance is z t, but 

z t=pt— p z 

=90 + 5-(90-4>) 



The Meridian Circle. 33 

Hence for the star to be visible at upper culmination 
we must have 

$ + <b <9o° 
or l<go — (p, 

hence the south declination of the star must be less 
than the colatitude. 

For example, at the latitude of Greenwich 51 28' 
38" -4 the colatitude is 3 8° 31' 2i ;/, 6, consequently all 
stars are visible at upper culmination at Greenwich 
which have a smaller south declination than 

~- 38 3i' 2i"-6 

and all stars are visible at both culminations which 
have a larger declination than 

+ 38 31' 2i"-6 

This statement requires a certain modification on 
account of refraction (§ 29), but this need not be 
further considered at present. 

§ 27. The Meridian Circle. — In most modern ob- 
servatories, the transit instrument described in § 17 is 
modified into a more useful instrument, called the 
meridian circle. By the aid of the meridian circle we 
are enabled to determine the declination of a star at 
the same time as we determine its right ascension. 

The principle of a meridian circle may be ex- 
plained by fig. 14. It consists primarily of a transit 
instrument a b, mounted with the usual precautions. 
Attached to the axis, near each of the pivots, there is 
a graduated circle, but only one such circle is shown 
in the figure. These circles turn with the axis of the 
telescope. Each circle is divided from o° to 359 , 

D 



34 



Astronomy. 



Fig. 14. 



each interval of one degree being again subdivided, 
111 the best instruments, into spaces of two minutes. 
For the general purpose of explaining the method of 
using the meridian circle, we shall suppose that the 
circles are simply read by the aid of a pointer x Y. 
This pointer is attached to the solid masonry pier 
which carries one of the bearings on which the pivots 
of the instrument turn. In actual use the reading 
of the circles is effected by microscopes, and is an 
operation of such intricacy that we shall not describe 
it. 

In the field of view of the telescope are the system 
of spider lines proper for a transit instrument and repre- 
sented in fig. 10. We have 
already pointed out the use of 
the vertical wires, and now we 
are going to show the use of the 
horizontal wire CD. As the 
star moves across the field, 
the observer, by means of a 
slow movement of the tele- 
scope, places the wire c d 
immediately over the star so 
that, in consequence of the 
diurnal motion, the star ap- 
pears to run behind the wire. The observer also 
takes the transits across the five vertical wires in the 
way already described. When the star has passed from 
the field, the observer then looks at the circles and 
observes the degree of the graduation which the 
pointer x y indicates. 

§28. Observation of the Nadir. — But this one 




Observation of the Nadir. 3 5 

reading of the circle is not sufficient to define the posi- 
tion of the star; we must now obtain a second reading 
with the telescope in a definite position. Thus, sup- 
pose in fig. 13 the direction in which the telescope 
was pointed was c t, then, if we were able to turn the 
telescope to p and read off the circle again, the differ- 
ence between the two readings would indicate the 
angular distance between the pole and the star, or 
what is called the polar distance of the star. 

There is, however, no star exactly at the pole, so 
that it is impossible to know when the telescope is 
pointed precisely towards the pole. We are therefore 
obliged to resort to a different process. Suppose that 
we were enabled to direct the telescope exactly to the 
zenith, then the difference between the two readings 
of the circle would give the zenith distance of the star. 
Here, again, we meet the same difficulty — how are 
we to know when the telescope is exactly pointed to 
the zenith? But though we are unable to accomplish 
this, we can do what is equally convenient, for we 
have a means of pointing the telescope exactly to the 
nadir. 

The surface of a liquid at rest is a perfectly hori- 
zontal plane. A perpendicular to such a surface 
points upwards precisely to the zenith, and down- 
wards precisely to the nadir. Now suppose we take 
a basin full of clean mercury, the surface is not only a 
horizontal plane, but it is also a brightly reflecting 
mirror. If we place this basin underneath the tele- 
scope, and turn the object glass of the telescope down 
towards the mercury, then when the system of wires 
are properly illuminated, we are able to see not only 



36 



Astronomy. 



Fig. 15. 



the wires themselves, but also their images reflected 
from the surface of the mercury. 

To show that this enables us to direct the tele- 
scope to the nadir, look at fig. 15. Let a b be the 
telescope, and p q the surface of the mercury, and let 
the small cross at o be the intersection of the wires. 
Now the rays of light diverging from the illuminated 
cross at o fall on the object-glass at b, and emerge 
thence in a parallel beam to 
fall on the surface of mercury 
p q. Draw r t perpendicular 
to the surface of the mercury 

\p q. Then by the laws of 
11/ reflection of light the beam 
HI after reflection from the mer- 

cury will proceed in a direc- 
tion r c, so as to make the 
angle trc equal to the angle 
t r b. It follows that in the 
circumstances depicted in the 
figure the reflected beam will 
not return to the telescope at all, nor will the reflected 
image of the wires be seen. 

But now suppose that the telescope • was placed 
with its axis very close to the line t r, then the reflected 
image would be visible in the field, and it would be 
possible to move the telescope until the reflected image 
of the cross is absolutely coincident with the cross itself. 
Under these circumstances w T e may be sure that the 
axis of the telescope is pointed exactly down to the 
nadir. 

While the telescope is directed towards the nadir, 




Zenith Distance. 



37 



we are to read off the circle again by the pointer, and 
the difference between the reading now obtained, and 
the reading when the telescope was pointed to the 
star, expresses exactly the angle through which the 
telescope has been turned when it is moved from the 
star to the nadir. This angle must evidently be equal 
to the supplement of the zenith distance of the star, 
and hence by this plan of observation the zenith dis- 
tance of the star has been determined. 

The important process of determining the zenith 
distance of a star may also be illustrated by fig. 16. 
The telescope in the FiG i6 

position x y points to- ,.* 

wards the centre of the 
earth (supposed spheri- 
cal). The tangent plane 
to the surface of the 
earth at t coincides with 
the surface of the mer- 
cury. Hence when the 
middle wire coincides 
with its reflected image, 
the axis of the telescope 
is directed towards the 
centre of the earth c. In the position a b the tele- 
scope is directed towards a star The angle s o c 
represents the angle through which the telescope must 
be turned, in order to be moved from the star to the 
nadir. Hence the angle x o s, which is the zenith 
distance of the star, is known. 

o q is parallel to the axis of the earth ; hence the 
angle xoq is equal to the angle t c p. This angle 




38 Astronomy. 

being the complement of the latit de is generally 
called the colatitude, and the angle qos, or the polar 
distance of the star, being equal to the sum of the 
zenith distance and the colatitude, is therefore known. 
The difference between the polar distance of the star 
and 90 is the declination. 

§ 29. Refraction. — The actual calculation of the 
true zenith distance of a star from the two observa- 
tions is not, however, quite so simple a matter as we 
have described. The apparent zenith distance of 
the star which we have determined is always some- 
what smiller than the real zenith distance, which is 
what we want to know. The difference between the 
real zenith distance and the apparent zenith distance 
is due to the presence of the atmosphere surrounding 
the earth. The real zenith distance is the zenith dis- 
tance which we should observe if there were no atmo- 
sphere ; the apparent zenith distance is what we actu- 
ally do observe. This effect of the earth's atmosphere 
is termed atmospheric refraction. 

Let c (fig. 17) represent the centre of the earth, 
p is a point upon the earth's surface, while the circle 
ltm is the bounding surface of the earth's atmo- 
sphere. Suppose there is a star in such a position 
that it would be seen in the direction p y by an ob- 
server at p if there were no atmosphere, and let us 
consider what difference will be produced by the pre- 
sence of the atmosphere. 

The ray v r, which, were there no atmosphere, 
would go straight to p, is deflected from its course 
when it meets the atmosphere, in consequence of the 
refracting power of the air. The ray y r being thus 



Refraction. 



39 



Fig. 17. 



deflected, will reach the surface of the earth at Q, and 
will thus not enter the eye of the observer at p. A full 
description of the phenomena of refraction exhibited 
by air in common with all transparent substances, may 
be found in works on Optics. 

All the rays of light which reach the earth from so 
distant a body as a star are practically parallel ; let 
us fix our attention upon the ray x t, which impinges 
upon the atmosphere at t, the direction x x being 
parallel to y p. The ray x t 
is then deflected along t p, 
so that this ray is visible 
to the observer at p, but to 
him the light is coming along 
the direction t p, and there- 
fore to him the star appears 
to be in the direction t s. 
If the line c p be produced 
up to the zenith, the observer 
at p will see the star with the 
zenith distance z p s, and this 
is what is actually shown with the meridian circle. It 
is however clear, that the real zenith distance is z p y, 
whence we see that the real zenith distance is always 
greater than the apparent. 

The angle s p y, by which the real zenith distance 
exceeds the apparent zenith distance, is called the 
refraction. 

For rays coming from a star at the zenith, the re- 
fraction is zero. As the zenith distance increases the 
refraction increases, nearly uniformly at first, and after- 
wards with an increasing rate until at the zenith dis- 




40 Astronomy. 

tance of 45 the refraction is 57 seconds. As the 
horizon is approached, the refraction increases much 
more rapidly, until at the horizon it amounts to no less 
than 35 minutes, or upwards of half a degree. 

We may here mention a somewhat remarkable 
consequence of refraction. If there were no atmo- 
sphere the sun would have completely risen when its 
lower edge was exactly 90 from the zenith ; owing to 
refraction, however, the lower edge will appear to be 
on the horizon when it is really 90 35 from the zenith. 
Now as the apparent diameter of the sun is less than 
35', it follows that the sun is really entirely below the 
horizon at the time when it appears, in consequence 
of refraction, to have completely risen. As refraction 
anticipates sunrise so it retards sunset, and the con- 
sequence is that refraction actually increases the length 
of the day. 

The amount of refraction at a given zenith distance 
depends to a small extent upon the temperature of the 
air and upon its barometric pressure. Into these de- 
tails, which are, however, of great importance to the 
practical astronomer, we do not at present propose to 
enter. 

We shall now show by what kind of observations 
astronomers have determined the amount of refraction 
at each zenith distance so accurately that they are 
able to allow for its effect on all observations, and 
thus obtain results nearly though not quite so accurate 
as they would obtain were they able to make their 
observations without the disturbance which refraction 
produces. 

§ 30. Calculation of Refractions.— Select a cir- 



Determination of Latitude. 41 

cumpolar star, and observe its apparent zenith distance 
z s, at its upper culmination (fig. 13). After an interval 
of about twelve hours, its apparent zenith distance z s' 
at its lower culmination can also be observed. Now if 
there were no refraction p s would be equal to p s' 
and therefore 

z p=4 (z s + z s') 

whence z'p would be determined. Now the quantity 
z p thus determined is the colatitude of the place, 
which is of course quite independent of the stars, so 
that we should get the same value for z p, whatever be 
the circumpolar star adopted. 

As a matter of fact, the values for z p obtained 
from different stars differ, and the amounts of the re- 
fractions are determined by the condition that when 
the proper correction is applied to each observation, 
the colatitudes determined from each star shall be 
equal. 

§ 31. Latitude. — We are now able to see how the 
latitude of the observatory is to be determined, for 
when by a multitude of observations of circumpolar 
stars the law of refraction has been accurately ascer- 
tained, we are able to determine how much the co- 
latitude obtained by the observations of any particular 
star has been affected by refraction, and thus we are 
enabled to determine the true colatitude. When the 
true colatitude is known, then it is of course easy to 
determine the latitude itself. 

By observations of this kind the latitude of an 
observatory can be determined accurately to a small 
fraction of a second. 



42 Astronomy. 



CHAPTER VI. 

THE APPARENT MOTION OF THE SUN. 

§ 32. The Sun appears to move among the Stars. 

Having now explained how the right ascension and 
declination of any celestial body can be determined 
by the meridian circle, we may conceive the process 
to be applied to the observation of the sun. When 
this is done we find that though the right ascensions 
and declinations of the stars remain constant (or very 
nearly so), the right ascension and declination of the 
sun are continually changing. We are then led to the 
conclusion that the sun must be continually changing 
its place upon the celestial sphere with reference to 
the stars. The bright light of the sun prevents us 
from seeing the stars in its vicinity on the celestial 
sphere, but if we could see them, then we should per- 
ceive that the sun was slowly moving day by day from 
west to east. 

That the position of the sun with respect to the 
stars on the celestial sphere is in a condition of con- 
stant change, may be inferred from ordinary observa- 
tions without any telescope at all. Everyone must have 
noticed that in summer at noon, the sun is high in 
the heavens, while in winter he is low. On the other 
hand every star reaches the meridian at the same alti- 
tude whatever be the season of the year. We thus see 
that the polar distance of the sun is greater in winter 
than in summer, or that the declination of the sun is 
continually changing. 



Motion of the Sun among the Stars. 43 

§ 33. Observation of the Pleiades. — We can also 
see by simple observation, though in a somewhat less 
direct manner, how the sun moves in right ascension. 
For this purpose it will only be necessary to look at 
the heavens at a fixed hour on a series of nights 
throughout the year, separated by intervals of perhaps 
two months. To give definiteness to these instructions 
you are recommended to look in the heavens for the 
Pleiades at 11 o'clock p.m. on the nights of January 
1st, March 1st, May 1st, July 1st, September 1st, 
November 1st, and to observe the positions in the sky 
in which this little group is found. If the weather 
prevent you from seeing the stars on any of the nights 
named, then you must take the next fine night. I 
shall now describe to you what you will see. I presume 
of course, that jou know the directions of north, south, 
east, and "west from the place where you are stationed. 
I imagine you to be placed in the northern hemisphere 
at about the latitude of the Middle States. On the 
1st of January you will see the Pleiades high up in the 
sky a little to the south of west. On the 1st of March 
they will be setting a little north of west. On the 1st 
of May they are not visible. On the 1st of July they 
are not visible. On the 1st of September they are 
visible low in the east. On the 1st of November they 
are high in the heavens a little to the south of east. 
On the next 1st of January they will be in the same 
position as they were on the same day last year, and 
so on through the whole cycle. It is exceedingly de- 
sirable for the pupil actually to make these very simple 
observations for himself. 

Let us now consider what information we gain 



44 Astronomy. 

from the results. It seems as if the Pleiades were at 
first gradually moving from the east to the west, that 
then they dipped below the horizon, and after a short 
time reappeared again in the east, so as to regain at 
the end of a year the position they had at the begin- 
ning. 

The reader will, it is hoped, not confuse the annual 
motion which we are here considering with the apparent 
diurnal motion which we considered in § 8. In the 
apparent diurnal motion the phenomenon is observed 
by looking out at different hours on the same night. 
To observe the apparent annual motion the observer 
should look at the same hour each night, but his ob- 
servations must extend over a year. 

We shall now examine somewhat more closely into 
the apparent annual motion. In the first place what 
does ii p.m. mean? It means that eleven hours have 
passed since noon ; i.e. since the sun was on the meri- 
dian (at least very nearly, we shall see the difference 
afterwards). Now we find that at eleven o'clock on 
the i st of March the Pleiades are farther from the 
meridian than they were at eleven o'clock on ist of 
January. But as the sun is at the same distance Cm 
time) from the meridian in the two cases, it follows 
that the Pleiades must be nearer to the sun on the 
i st of March than on the ist of January. It is, 
therefore, plain that the relative position of the sun 
and the Pleiades on the surface of the heavens must 
be changing. By comparing the sun in the same way 
with any other stars, it is found that the stars to the 
east of the sun are gradually approaching the sun. 
But we have already noticed that the positions of the 



The Ecliptic. 45 

stars inter se do not change, and therefore we are obliged 
to come to one of two conclusions ; either, firstly, that 
all the stars in the universe have an annual motion 
from east to west relatively to the sun, which remains 
fixed, or that the sun has an apparent annual motion 
from west to east, while the stars remain fixed. 

§ 34. The Ecliptic. — We snail now suppose that by 
the meridian circle the right ascension and declination 
of the sun has been determined for a large number of 
days throughout the year. We shall then be able to 
plot down upon a celestial globe the actual spot occu- 
pied by the centre of the sun on the celestial sphere 
for each day on which observations have been secured. 
When this is done, it is found that all the points thus 
marked lie in a plane, and that this plane passes 
through the centre of the globe. This proves that the 
apparent annual path of the sun in the heavens is a 
great circle. 

This great circle is called the eclptic. The con- 
stellations which lie along its track are known as the 
Signs of the Zodiac. The ecliptic is inclined to the 
celestial equator at an angle of 23 27'. This is 
called the Obliquity of the Ecliptic. Each point on 
the ecliptic corresponds to a certain day in the year, 
i.e. the day on which the sun is situated in that point 
of its annual path. The ecliptic intersects the equator 
in two points ; when the sun is situated in either of 
these points, the length of the day is equal to the 
length of the night These two points are conse- 
quently called the Equinoxes. 

The equinox through which the sun passes on 
2cth March is called the Vernal Equinox, and at 



46 Astronomy. 

this point the sun's declination is zero. The vernal 
equinox is one of the most important points on the 
celestial sphere, and, when it is on the meridian, an 
accurately adjusted sidereal clock should show o h 
o m o s . The importance of the vernal equinox in 
astronomy arises from this, that the right ascension 
of any star is equal to 'the interval of sidereal time 
between the moment of the transit of the vernal 
equinox and the transit of the star in question. 



CHAPTER VII. 

SIDEREAL TIME. 



§ 35. Sidereal Day. — We are now going to consider 
the very important subject of sidereal time with more 
detail than has been possible in the few references 
which we have hitherto made to it. The first question 
to be considered is, what is really meant by a sidereal 
day. 

We have said that the sidereal day is the interval 
between two successive culminations of the same star. 
Let us for the sake of example fix our attention upon 
the bright star Sirius. Now the interval between the 
culminations of Sirius on 1st January and 2nd January, 
1877, is 24 11 o m 0*007° of sidereal time. Is this 
interval constant or not ? If we repeat the observa- 
tions on the 1st and 2nd of March we find for the 
interval 23 h 59 m 59*985 8 . Now it is true that 
each of these quantities only differs by an extremely 



Sidereal Day. 47 

small fraction of a second from twenty-four hours, but 
there still is a difference. Let us now compare the in- 
terval between two successive culminations of another 
bright star, Vega, with what we have already found. It 
appears that the interval between the successive cul- 
minations of Vega on 1st January and 2nd January, 
1877, is 24 11 o m o s *oi3 

The reader will probably here observe that there 
must surely be something incorrect in the theory that 
the apparent diurnal motion is really due to the rota- 
tion of the earth upon its axis, for if this were the case 
the period should obviously be absolutely the same 
for all stars. To this we reply, that if we could see 
the real culminations of the stars the intervals of the 
successive culminations would be exactly the same 
for each star and constant for each one, but that the 
apparent culminations which are what alone we can 
see are affected by certain sources of error which are 
now understood. When due allowance is made for 
the effect of these errors it is then found that the in- 
terval between two successive culminations is the same 
for each star, and, allowing for what is called proper 
motion, that it is constant for each star at least for 
many centuries. 

This constant interval of time it is which is called 
the sidereal day. Thus the sidereal day is really the 
period of the revolution of the earth upon its axis. It 
is possible that the length of the sidereal day may be 
increasing, though with such extreme slowness that it 
need not be considered at present. 

The sidereal day is divided into twenty- four hours, 
each hour is divided into sixty minutes, and each 
minute into sixty seconds. 



48 Astronomy. 

§ 36. Setting a Sidereal Clock. — We have now to 
explain how the sidereal clock is to be set so that it 
shall show correct sidereal time ; in other words, we 
have to show how we can ascertain the time shown by 
our clock when the vernal equinox is on the meridian, 
i.e. the error of the clock. 

It will be desirable (indeed necessary) to make this 
determination in or close to the time at which the sun 
is situated in one or other of the equinoxes. To give 
definiteness, I shall suppose that the sun is approach- 
ing the vernal equinox, and that for example on 19th 
March, 1877, we commence our observations. The 
sun is observed at transit with the meridian circle, and 
the declination found to be — o° 23' 2i/ /# 9. The 
moment as shown by the clock at which the centre of 
the sun was on the meridian is also determined. The 
observation is repeated on the following day when 
the declination of the sun is found to be + o° d 20 //# 4. 
It therefore follows that somewhere between noon on 
the 19th and noon on the 20th, the sun passed from 
having a south declination to having a north declina- 
tion, that is, the centre of the sun must have passed 
through the point where it had no declination, that is, 
of course, through the equinox. Now as we know the 
declinations at the times of the two observations it is 
easy to calculate the time when the declination was 
zero. We thus know the time by our sidereal clock 
when the sun was on the equinox. If the sun hap- 
pened to be on the equinox at the moment of culmina- 
tion, then of course the clock should show o h o m o s 
at the instant of culmination, and the actual time 
shown by the clock would be the error of the clock. 



The Sidereal Clock. 49 

It will, however, generally happen that the time of 
the sun's passage through the equinox does not coin-, 
cide with the time of the sun's culmination, and 
consequently the sun will have moved away from the 
equinox in the interval which elapses between his 
passage through the equinox and the next succeeding 
culmination. The equinox will therefore culminate 
sooner than the sun, but we know the rate at which 
the sun is moving, and hence we know how far it will 
have moved from the equinox at the time of culmi- 
nation. Hence from having observed the time of 
culmination of the sun by our clock we are able to 
compute the time of culmination of the equinox, 
whence we deduce the error of the clock. 

We have now to explain the practical method by 
which the operation of determining the error of the 
sidereal clock is greatly facilitated. The process we 
have described, though the only absolute method, is 
yet exceedingly inconvenient for ordinary purposes. 
In our climate, culminations of the sun cannot be 
very frequently observed, and further, these opera- 
tions can only be performed when the sun is at one 
of the equinoxes. 

Suppose, however, that on one occasion we have 
succeeded in determining accurately the error of our 
clock in the way we have described. We then observe 
a bright star with the transit instrument or meridian 
circle, and we determine the instant of its culmination. 
The clock- time when properly corrected is really the 
right ascension of the star. It is in fact the interval 
between the time of culmination of the equinox and 



So Astronomy. 

the time of the culmination of the star. Now does 
this interval of time remain constant? We may 
assume that the place of the star on the celestial 
sphere remains constant with respect to all the other 
stars. If then the position of the equinox with respect 
to all the stars remained constant, the right ascension 
of the star would remain constant. But as we shall see 
hereafter that the equinox is not absolutely fixed with 
respect to the stars, for it has a slow motion which in 
the course of years becomes very perceptible. The 
effect of this is, that the right ascension of a star 
is slowly but continually altering. Now the amount 
of this alteration is well ascertained ; hence, if we 
know the right ascension of a star at one date we can 
calculate what the right ascension of the same star is 
at any other given date. 

If, therefore, a number of stars be observed when 
the clock is correct, we have the means of finding 
the true right ascension of these stars for any 
subsequent date. In the ' Nautical Almanac ' for 
each year a list of about 150 stars is given with the 
right ascension of each star at intervals of every 
ten days. It is by the aid of these stars that astro- 
nomers set their sidereal clocks, and the process is as 
follows : — 

By referring to the c Nautical Almanac ' the astro- 
nomer will always find a star which will shortly come 
on his meridian ; he then makes an observation with 
the transit instrument or meridian circle of the 
moment of culmination of this star by his sidereal 
clock. This is compared with the right ascension as 
given in the * Nautical Almanac/ and the difference 



The Sidereal Clock. 5 1 

between the two is the error of the clock. Thus, for 
example, we have for Vega from the ' Nautical Al- 
manac ' — 



1877. 



If the sidereal clock at any observatory show i8 h 
32™ 5i s, 42 at the instant of culmination of Vega on 
3rd July, then the correction which must be applied to 
the clock time is — i s, g6. 





Right Ascension. 




h. m. s. 


Jan. 1 . 


. 18 32 44-85 


April 2 . 


. l8 32 47*28 


July 3 • 


. l8 32 49*46 


Oct 2 . 


. 18 32 48-13 



CHAPTER VIII. 

MEAN TIME. 



§ 37. Mean Time. — The reader may perhaps think 
that needless complexity is introduced by using one 
kind of time for astronomical purposes and another 
kind of time for ordinary civil purposes. We proceed 
to explain the reason why this distinction must be 
maintained. 

The great convenience of astronomical time con- 
sists in this, that each star culminates every day at 
the same sidereal time (subject only to minute varia- 
tions). But for the ordinary purposes of life sidereal 
time would not answer. We are obliged to regulate 

£ 2 



52 Astronomy. 

civil time by the sun, and custom has decreed that at 
the moment when the Sun culminates (or to speak 
more accurately, when the mean Sun, to be hereafter 
explained, culminates) our ordinary clocks should 
show noon or o h o m o s . Now, the moment of culmi- 
nation of the Sun, as shown by a sidereal clock, 
would be different every day because the Sun is 
moving from west to east among the stars, so that 
compared with the stars it comes on the meridian 
about four minutes later every day. We are, there- 
fore, obliged to have a mean time clock, the going o 
which is regulated by the Sun, while the sidereal 
clock is regirated by the stars. 

§ 3 8 - Apparent Solar Day. — We have now to 
explain a little more fully what is to be understood by 
mean solar time. If we observe the transit of the 
centre of the Sun across the meridian to-day, and if 
we make the same observation again to-morrow, the 
interval between the two observations is an apparent 
solar day. We first notice that the apparent solar day 
as thus defined is not constant. 

For example, taking four days as nearly as possible 
equidistant throughout the year, viz., ist January, 2nd 
April, 3rd July, 2nd October, we have the following 
apparent solar days or intervals (in mean solar time) 
between the culmination of the Sun on the days 
named and on the following days : — 

h. 

1877. Jan. 1 to 2 . .24 

April 2 to 3 . .23 

July 3 to 4 . .24 

Oct 2 to 3 . .23 



m. 


s. 


O 


28 


59 


42 





10 


59 


41 



Apparent Solar Day. 53 

It will be noticed that the first of these apparent 
solar days is 47 s longer than the last. We adopt as 
the definition of a mean solar day the average interval 
between two successive culminations. 

§ 39. The Mean Sun. — We now introduce a con- 
vention which is known as the mean Sim. Suppose 
that we had an imaginary sun moving uniformly in 
the equator and completing its revolution in the same 
time as the true Sun, then when this mean sun is on 
the meridian, the properly adjusted mean solar clock 
should show noon. Thus the mean sun and the true 
sun will generally differ slightly in the times at which 
they arrive on the meridian, and the difference of the 
times is called the equation of time. 

§ 40. Mean Time at Apparent Noon. — The fol- 
lowing table exhibits (for each of the four dates already 
referred to) the time which should be shown by a 
mean- time clock which is going correctly, when the 
real Sun is on the meridian of Greenwich. 

m. s. 

4 o*32 

3 3372 

3 55-8i 

49 14-53 

For example, on January 1, 1877, the real Sun 
crosses the meridian of Greenwich at 4 m o s *32 p.m. 
The equation of time on that day is therefore 4 m 

8 *32. 

§ 41. Determination of the Mean Solar Day. — 

We shall now consider the very important problem of 
determining the mean solar day. 

J3y observations of the stars the error of the sidereal 







h. 


1877. Jan. 1 . 


• 


O 


April 2 . 


• 


O 


July 3 • 


• 


O 


Oct. 2 . 


. 


II 



54 



Astronomy. 



clock in the observatory can be determined. Sup- 
pose that we have rated our sidereal clock to go cor- 
rectly, and that we observe the transit of the centre 
of the Sun across the meridian, we thus obtain the 
right ascension of the Sun. Let us suppose, for the 
sake of illustration, that these observations have been 
made upon the dates here given : — 

Apparent Right Ascension of the Sun at Apparent 
Noon. 



1875. Jan. 1 

1876. Jan. 1 

1877. Jan. 1 
April 2 

July 3 

Oct. 2 

1878. Jan. 1 



h. m. s. 

l8 46 41 

18 45 37 

18 48 59 

o 47 19 

6 50 24 

12 34 27 

18 47 54 



It is evident that from the apparent noon on 
January t, 1877, to the apparent noon on January 1, 
1878, 365 apparent solar days have elapsed; during 
this time the sidereal clock shows an interval of 366 
days very nearly, or more accurately of 365 days 23 
hours 58 mins. 55 sees. Hence the average length of 
one of 365 consecutive apparent solar days in sidereal 
time is 

365 days 23 hours 58 mins. 55 sees. 

365 
= 2 4 h 3 m 57 s . 



When the average length of each of a great numbei 



Sidereal Time of Mean Noon. 55 

(say 100,000) of coilsecutive apparent solar days is 
taken, the mean length expressed in sidereal time is 
slightly different from the result we have found, and is 

M h 3 m 56'5554 9 . 

This is therefore the equivalent in sidereal time 
to one mean solar day. 

§ 42. Determination of the Sidereal Time at Mean 
Noon. — The hypothetical mean sun is on the meridian 
every day at mean noon. The interval between two 
consecutive returns of the mean sun to the meridian 
is equal to the length of the mean solar day. Sup- 
pose the mean sun comes to the meridian a seconds 
later every day, it follows that if A represent the right 
ascension of the mean sun at mean noon on a certain 
day that the right ascension of the mean sun at mean 
noon n days later will be 

A + nd. 

Hence we form the following table for the right 
ascension of the mean sun : — 

Right Ascension of Mean Sun at Mean Noon. 

1877. Jan. 1 . A 

Apl. 2 . A + 91 d. 

July 3 . . A + 183 d. 

Oct. 2 . A + 274 d. 

Now we want to make the mean sun, while still 
moving uniformly in right ascension, conform as far 
as this imperative restriction will permit with the 
actual motion of the true sun. We therefore compare 
the table just given with the table of § 41, and we 



56 Astronomy. 

seek to determine A so that thes£ tables shall coincide 
as far as practicable. Now as we know d to be 3 m 
5 6 *5 5 54 s we can determine the value which A should 
have for each of the four dates so that the two right 
ascensions should coincide. The four values of A 
thus found are 



Jan. i 


• 


. 18 


48 


S9 


Apl. 2 


• 


. 18 


48 


33 


July 3 


• 


. 18 


48 


55 


Oct. 2 


• 


. 18 


34 


11 


and the mean of these values is 








i8 h 


4S m 9 9 . 







When the value of A is computed from a very 
large number of observations, the value just given is 
slightly modified, and we have as the true sidereal 
time at mean noon on January 1, 1877 

i8 h 44^ 57 s 72. 

As we now know the sidereal time at mean noon 
on one day we are able to compute it for any other 
day. 

Example. — Find the sidereal time at mean, noon 
on February 11, 1878. Since 406 mean solar days 
have elapsed since January i s 1877, the mean sun has 
gained in right ascension 

406 x 236 s, 56 = 26 11 4o m 42 s , 

hence the sidereal time at Greenwich mean noon on 
nth February is 

i8 h 44 m 58 s + 26 h 4o m 42 s -2i h 25 111 40 s . 



Determination of Mean Time. 57 

§ 43- Determination of Mean Time from Sidereal 
Time. — In astronomical "ephemerides " the sidereal 
time at mean noon on some standard meridian is given 
for each day of the year. In the American Epheme- 
ris it is given for two meridians, that of Greenwich 
and that of Washington. 

Example. — It is required to determine the mean 
time at Washington corresponding to 23 11 i m 18 s of 
sidereal time on February 11, 1878. From the Amer- 
ican Ephemeris and Nautical Almanac for 1878, p. 
324, we see that the sidereal time of Washington, 
mean noon, on the day in question is 2i h 26 m 30 s , 
hence the required mean time is i h 34 111 48 s of 
sidereal time past mean noon ; diminishing this by 
tt&Ws of its whole amount, or using Table VI. at the 
end of the Ephemeris, we find that an interval of i h 
34 m 48 s of sidereal time is equal to i h 34 111 32.5 s of 
mean solar time. The correct mean time corre- 
sponding to the given sidereal time is therefore i h 34 m 
32.5 s P.M. 

§ 44- Determination of Mean Time at a Given 
Longitude. — The calculation just described must be 
slightly modified when it is desired to compute the 
mean time corresponding to a given sidereal time at 
a place which does not lie upon the meridian of 
Washington. The quantity which is given in the 
1 American Ephemeris* as the sidereal time of mean 
noon, is the right ascension of the mean sun when it 
is on the meridian of Washington, but as the mean 
sun is continually changing its right ascension it fol- 
lows that the sidereal time of mean noon must depend 
upon the meridian which is under consideration. 



58 Astronomy. 

We may here make a remark with reference to the 
method of estimating longitudes : for example, when 
it is stated that the longitude of Chicago is 42™ 14 s 
west of Washington the statement may be interpreted 
in two ways, both of which are correct. It may mean 
that an interval of 42™ 14 s of sidereal time will elapse 
between the transit of a fixed star across the meridian 
of Washington and the transit of the same star across 
the meridian of Chicago, or it may equally mean that 
an interval of 42 ra 14 s of mean solar time will elapse 
between the transit of the mean sun across the meri- 
dian of Washington and the transit of the mean sun 
across the meridian of Chicago. 

Example. — Find the sidereal time at mean noon 
at Chicago upon February 11, 1878. The meridian 
of Chicago is 42 111 14 3 west of Washington, conse- 
quently the mean sun will be increasing its right 
ascension during the mean solar interval of 42™ 14 s 
before it gets to the meridian of Chicago. Now sup- 
pose that a fixed star and the mean sun came on the 
meridian at the same time at Washington, then the 
right ascension of the star is the sidereal time at mean 
noon at Washington ; but when the star reaches the 
meridian of Chicago, which it does in an interval of 
42 m 14 s of sidereal time, the mean sun has not yet 
reached the meridian on account of its motion in the 
interval, and therefore the sidereal time at mean noon 
at Chicago is not the right ascension of the star ; but 
as the mean sun is on the meridian at Chicago in 42 m 
14 s of mean solar time the difference between the side- 
real time at mean noon at Washington and at Chicago 
is equal to the interval of sidereal time corresponding 



Length of the Year. 59 

to the difference between 42 111 14 s of mean solar time 
and 42 m 14 s of sidereal time, i.e. to 7 s nearly. Hence 
the sidereal time of mean noon at Chicago on Febru- 
ary 11, 1878, is 

2I h 2 6 m 37 s . 

§ 45. The Year. — We may here point out how 
the length cf the year is to be accurately determined. 
It has been found that the mean sun gains 3 ra 56 -5 5 54 s 
in right ascension in one mean solar day, hence the 
mean sun will gain 24 11 , i.e. perform one complete re- 
volution with respect to the equinox in 



24 

7s = 3 6 5' 2 42i days. 



3 m 56 5554 s 



CHAPTER IX. 

THE PLANETS. 



§ 46. Meaning of the word Planet. — We have 
already ascertained that the sun appears to move 
through die stars in a great circle called the ecliptic, 
the motion being completed in one year. But as the 
sun is much nearer to us than the stars, this apparent 
motion might be explained by the supposition that 
the sun was really at rest while the earth was in mo- 
tion round the sun. The sun appears to move from 
west to east among the stars, but precisely this ap- 
pearance could be produced by a real motion of the 



60 Astronomy. 

earth from east to west. It is, therefore, necessary 
for us to enquire which of these two explanations of 
the apparent motion is the correct one. 

In connection with this question it will be desir- 
able for us to consider some of the other celestial 
bodies which are termed the planets. We have already 
referred to the apparent fixity of the stars in their 
relative positions in the celestial sphere. The ob- 
server of the heavens will, however, notice a few 
objects which, though closely resembling the brighter 
fixed stars at a superficial glance, are yet of an entirely 
different nature. The most conspicuous feature of 
the class of objects to which we here refer is their 
apparent motion, and it is for this reason that they 
have been called planets. Of these objects there are 
five easily visible to the unaided eye at the proper 
seasons for seeing them. The names of these 
planets are Mercury, Venus, Mars, Jupiter, and Saturn. 
They were all well known to the ancients, and their 
movements appear to have attracted attention from 
the earliest times. The observer who is not provided 
with a globe or maps, and who is unacquainted with 
the heavens, might easily confuse the planets with the 
brighter stars. If, however, he had the use of a tele- 
scope, he would at once be able to tell the difference 
between one of these planets and a star. The stars, 
even in the largest and best telescopes, are little more 
than bright points of light. The planets, on the other 
hand, show a clearly defined disk, and suggest imme- 
diately to the observer that they are spherical, or 
nearly so. Even without a telescope, if the observer 
watch a planet for a few nights, and carefully compare 



Motion of Venus. 6 1 

its position by alignment with the stars in its vicinity, 
he will detect its motion. 

§ 47. Motion of the Planet Venus. — We shall 
now fix our attention upon the planet Venus, and we 
shall inquire more closely into the nature of its mo- 
tion. To make the observations which we shall here 
describe, it will not be necessary for the observer to 
use a telescope. 

Shortly after sunset, at the proper season, Venus 
appears like a brilliant star in the west. On subse- 
quent evenings, the distance between Venus and the 
sun gradually increases until the planet reaches its 
greatest distance, when it is about 47 from the sun. 
Venus then begins to return towards the sun, and 
after some time becomes invisible from its proximity 
to the sun. Ere long the same planet may be seen 
in the east, shortly before sunrise. It gradually rises 
more and more before the sun, until again Venus 
reaches the greatest distance from the sun, after which 
it commences to return, again passes the sun, and 
may be seen at evening in the west, as before. 

It thus appears that Venus is continually moving 
from one side of the sun to the other, and the ques- 
tion is how these movements are to be explained. It 
is noticed that when Venus is at its greatest distance 
from the sun, its apparent movement is much slower 
than when it is nearer the sun. It is further seen by 
the telescope that when Venus is at its greatest dis- 
tance from the sun it appears half illuminated, like 
the moon at first quarter. It is also on very rare 
occasions seen to pass actually between the earth and 
the sun, the phenomenon being known as the Transit 



62 Astronomy. 

of Venus, in which case the planet appears like a dark 
spot upon the surface of the sun. 

From all these facts it is inferred that the planet 
Venus is really a dark globular body, which moves 
around the sun in 224 days, in an orbit of a shape 
which we shall presently consider. As the sun exe- 
cutes its apparent motion among the stars, the planet 
seems to accompany it, alternately appearing to the 
east and the west of the sun, and never more than 47 
distant therefrom. 

§ 48. Apparent Motion of the Planet Mercury. — 
Precisely similar, though on a smaller scale, are the 
apparent motions of Mercury. This planet does not 
go so far from the sun as Venus, its greatest distance 
or elongation, as it is called, being only 2 8°. The 
time in which Mercu revolves round the sun is 87 
days. 

§ 49. The Earth is really a Planet. — We thus see 
that there are two planets, Mercury and Venus, which 
certainly appear to move round the sun. Now if we 
compare Mercury or Venus with the earth, we find 
some striking points of resemblance. All three bodies 
are approximately spherical, and they are all depen- 
dent upon the sun for light. It is, therefore, not at 
all unreasonable to inquire whether the analogy be- 
tween the three bodies may not extend further. Now 
we have already seen that the phenomena of the ap- 
parent annual motion of the sun could be explained 
by supposing that the sun is really at rest, and that the 
earth moves round the sun. When we combine this 
fact with the presumption afforded by the analogy 
between the earth and Mercury and Venus, we are led 



The Earth a Planet. 63 

to the belief that the earth, Mercury and Venus, are 
all bodies of the same general character ; and all agree 
in moving around the sun, which is the common 
source of light and heat to the three bodies. 

We are now enabled to take a further step in 
the knowledge of the planetary system, and to deter- 
mine, approximately at least, the forms of the orbits 
in which the planets revolve. 

§ 50. The Earth's Orbit is nearly Circular. — 
Whichever explanation of the apparent annual motion 
of the sun be adopted, one thing is evident, and that 
is that the earth's distance from the sun does not 
greatly vary. This is manifest from the consideration 
that the angle which a diameter of the sun subtends 
at the eye, or the apparent size of the sun, remains 
practically constant. If, therefore, we admit that it is 
really the motion of the earth round the sun which 
produces the apparent motion of the sun among the 
stars, we must admit that the earth in its motion re- 
mains pretty much at the same distance from the sun, 
i.e. that the earth must move very nearly in a circle 
which has the sun at its centre. 

It is also easily established by observation, that 
though the rate at which the sun is apparently moving 
in the ecliptic is not quite constant, yet that it is very 
nearly constant. It therefore follows that the real 
motion of the earth in its approximately circular orbit 
must be approximately uniform. 

§ 51. The Orbit -of Venus.— The consideration of 
the annual motion of the earth suggests to us to try 
whether the motions of Venus and of Mercury cannot 
be explained by the supposition that each of them 



6 4 



Astronomy. 



Fig. 18. 



moves nearly uniformly in a nearly circular orbit 
about the sun as a centre. When this attempt is 
made, it is seen that the principal features of the 
motions of Venus and Mercury can be explained with 
great facility. 

Let s (fig. 1 8) represent the sun. The inner of 
the two circles atvb represents the orbit of Venus, 
and the outer circle elm represents the orbit of the 
earth. 

We shall, in the first place, neglect the motion of 
the earth, and consider the appearances which would 

be produced by the motion 
of Venus. We shall then 
show how these appear- 
ances would be modified 
by taking account of the 
motion of the earth. 

Let us then suppose the 
earth stationed at the point 
l, and that Venus is at the 
point marked v, moving in 
the direction of the arrow. 
From l draw the tangent 
Then, as Venus is moving 
towards the tangent l t, the planet will appear to an 
observer stationed at l to be moving awaj r from the 
sun, inasmuch as the angle vl s is continually in- 
creasing. As Venus approaches t, it gradually gets 
farther from the sun, until at t it appears to have 
reached its greatest distance from the sun. The 
planet is there said to be at its greatest elongation ; 
and in the case of Venus, the angle tl s is equal 




lt to the orbit of Venus. 



Motion of Venus. 65 

to 47 . As Venus continues its motion it again 
begins to return towards the sun, until in the position 
a it passes between the earth and the sun. Still 
moving on, it reaches the point Q, which is the point of 
contact of the second tangent drawn from l. Venus 
then appears at its greatest distance on the other side 
of the sun, after which it again appears to draw near 
the sun, to pass behind it at b, and then to return to v 
to recommence the cycle which we have described. 
We thus see that the supposition of the circular 
motion of Venus explains the observed succession of 
the appearances of Venus as seen by the unaided eye. 

§ 52. Telescopic Appearance of Venus explained. 
We shall now consider how the telescopic appear- 
ances presented by Venus are to be explained. When 
the planet occupies the position v, that hemisphere of 
it which is directed towards the sun at s is illuminated 
by the sun light, but the other half of the planet is in 
darkness. Now, when the observer at l looks through 
a telescope, he is able to see the actual disk of the 
planet ; and as the hemisphere of Venus turned 
towards the observer is somewhat different from the 
hemisphere turned towards the sun, only a portion of 
the hemisphere seen by the observer is illuminated ; 
and, consequently, Venus appears to him not as an 
entire bright circle, but only as a portion of a circle. 
In fact, the observer is immediately reminded of the 
appearance of the moon, for all the phases of the 
moon are reproduced in miniature in the revolutions 
of Venus. 

As Venus approaches t, less and less of the illu- 
minated hemisphere is visible to the observer at l, and 

F 



66 Astronomy. 

so Venus gradually becomes a narrow crescent, like 
the moon as seen in the west shortly after new moon. 

When Venus reaches a, only its dark hemisphere 
is directed towards l, and, consequently, it is invisible. 
On rare occasions, however, Venus can be seen even 
in this position. We have spoken of the orbit of 
Venus as if it were exactly in the same plane as the 
orbit of the earth ; this, however, is not quite the case, 
for the planes of the two orbits are inclined at a 
small angle. If these two planes did really coincide, 
then whenever Venus was at a, it would be visible to 
the observer at l as a dark spot against the bright 
face of the sun. Owing to the fact that the plane of 
Venus's orbit is not exactly the same as the plane of 
the earth's orbit, it follows that when Venus is at a, it is 
usually slightly above or below the line drawn from l 
to s, and, consequently, is not seen. When Venus 
does actually come between the earth and the sun, the 
phenomenon is known as the Transit of Venus. (§ 68.) 

After passing a, Venus again presents the cres- 
cent-shaped appearance. Now, if we draw the line 
l x y from the point l, Venus will appear to be in the 
same position, whether it be at x or at y, the only 
difference being that at x Venus is moving from the 
sun, while at y Venus is moving towards the sun ; but 
the telescope at once reveals a wide difference between 
the appearances at x and at y. At x Venus is a nar- 
row crescent, and at y it is nearly full. This is of 
course explained by the different aspect which the illu- 
minated hemisphere of Venus turns towards the earth 
in the two cases. In the neighbourhood of b, Venus 
would appear quite full if we could see it, but the 



Motion of Venus. 6? 

proximity of the bright light of the sun renders Venus 
invisible in this position. 

§ 53. Effect ofthe Annual Motion of the Earth on 
the Appearance of Venus. — We shall now briefly con- 
sider what effect the annual motion of the earth in its 
orbit round the sun will have upon the apparent 
motions of Venus which we have been describing. 
For simplicity, we shall suppose that the orbits of the 
earth and Venus lie in the same plane. Now it is 
only the relative positions of Venus and the sun which 
we are considering \ and the relative position at any 
time is completely defined by the angular distance 
between the sun and Venus, as seen by an observer 
upon the earth. Now conceive that the orbits of 
both the earth and Venus are rotated about the sun, 
the axis of rotation being perpendicular to the plane of 
the orbits; conceive also that the earth and Venus, 
in addition to their own motions in their orbits, are 
carried round by the rotation of the orbits, then it 
is plain that this rotation will not in the least affect 
the relative position of Venus with respect to the sun. 
Suppose, for the sake of illustration, that two pas- 
sengers are walking on the deck of a ship round the 
mast, their relative positions do not in the least depend 
upon the motion of the ship as a whole. 

Now imagine that the motion of rotation which we 
have supposed to be imparted to the two orbits takes 
place in the same time as the actual rotation of the 
earth around the sun (365*26 days), and in the oppo- 
site direction. The effect upon the relative motion 
will be unaltered. The effect upon the earth will be 
to bring it to rest. But what will be the effect on 

f 2 



68 Astronomy. 

Venus ? Since the time which Venus takes to accom- 
plish its orbit is 2247 days, it follows that in one day 

it would move through an angle equal to ^ . But 

2247 

in the hypothetical motion which we have assumed 

for the purpose of bringing the earth to rest the 

orbit of Venus would be turned through -? — - in 

365*26 

one day. Hence, in one day, Venus would actually 

gain on the earth an angle equal to 

3 60 360 
2247 365-26 

It follows that the number of days in which Venus 
would appear, when viewed from the earth, to have 
accomplished a complete revolution about the sun is 

360° 



360 360 



=S83-9 



224-7 36526 

Hence we see that the effect which the real motion 
of the earth has upon the apparent motion of Venus 
is to increase the time of its revolution, but not other- 
wise to alter the general circumstances of the motion. 

§ 54. The Orbit of Mercury. — The orbit of Mer- 
cury possesses the same general features which we 
have described in the case of Venus. These two 
planets are the only planets hitherto discovered which 
circulate round the sun in orbits lying inside the orbit 
of the earth. The success which we have found in 
the attempt to explain their motions by the supposi- 
tion that they move in nearly circular orbits, suggests 



Motion of Mars. 69 

to us to try whether the apparent motions of the 
other planets may not equally be explained by the 
supposition that they revolve around the sun in nearly 
circular orbits larger than the orbit of the earth, and 
therefore surrounding it. 

We should here first observe, that all the five prin- 
cipal planets are invariably to be found in or near to 
that great circle of the celestial sphere which is called 
the ecliptic* Now as the apparent motion of the sun 
in the ecliptic is really due to the motion of the earth, 
it follows that the orbit of the earth must lie in the 
plane of the ecliptic. As the planets never depart far 
from the plane of the ecliptic, it must follow that their 
orbits must lie very nearly in the same plane as the 
plane of the earth's orbit. 

§ 55. The Apparent Motions of Mars. — We shall 
now endeavour to explain the apparent motions of 
Mars on the supposition that it moves in a nearly cir- 
cular orbit about the sun. As the periodic time of 
Mercury in its orbit is 87*97 days, of Venus 2247 
days, and of the earth 365*26 days, it would appear that 
of two planets that which has the greater periodic time 
is at the greater distance from the sun. It is therefore 
reasonable to suppose that Mars, which has a greater 
periodic time than the earth, is more distant from the 
sun than the earth. We shall suppose that the outer 
of the two circles in fig. 19 represents the orbit of 
Mars, while the inner one is the orbit of the earth, s 
being the sun in the centre. Now, just as w r e showed 
that the appa?-ent movements of Venus were unaltered 
by supposing the earth to be at rest and Venus to be 
moving with a slower motion, so now we may suppose 



?o 



Astronomy. 



Fig. 19. 



Xi 



Mars to be at rest at m, and the earth moving in its 
orbit with a correspondingly slower motion. 

Let us first suppose the earth to be at x, then 
Mars, which is situated at m. will be seen in the direc- 
tion x m, and will be referred to the stars in the posi- 
tion p. As the earth moves on in the direction 
towards c, Mars appears to move towards h, but this 
motion will gradually become more slow until at the 
moment when the earth reaches b, which is the point 
of contact of the tangent 
drawn from m, the motion of 
Mars will apparently cease. 
As the earth passes from b 
towards y, Mars will begin 
to move backwards, so that 
when the earth arrives at y, 
Mars will have returned to Q , 
as the earth approaches a, 
Mars will move gradually to- 
wards k, so that when the 
earth reaches a Mars will have 
reached k, after which it will gradually return again 
towards h. 

We thus see that if the motion of Mars be such as 
we have supposed, we should expect to find that the 
planet sometimes appears to be moving in one way, 
sometimes in another way, and sometimes to remain 
stationary. Now as all these varieties are seen in the 
motion of Mars, it follows that there is a presumption 
that the orbit of Mars, like that of Mercury or Venus, 
is very nearly circular. 




7i 

CHAPTER X. 
kepler's laws. 

§ 56. Orbits of the Planets are not Perfect Circles. 
We have hitherto only been considering such general 
features of the movements of the planets as can be 
observed without the aid of telescopes, or with merely 
such optical power as is necessary to reveal the crescent 
appearances of the interior planets. We have now to 
discuss the more accurate knowledge which has been 
the reward of a more careful and detailed study of 
the movements of the planets with suitable measuring 
instruments. 

By the aid of the meridian circle it is possible to 
determine a series of positions of a planet at different 
times, and thus to mark these positions on the celestial 
sphere with precision. When this is done it is found 
that although the general features of the motions are 
consistent with the supposition that the orbits are 
perfect circles, yet that when a more minute compa- 
rison is instituted between the results of this supposi- 
tion and the results of actual observation, certain dis- 
crepancies are brought to light which are too large and 
too systematic to admit of being explained away as 
mere errors of observation. 

§ 57. Kepler's First Law. — Kepler was the first 
to discover that the discrepancy between observation 
and calculation could be removed by the supposition 
that the planets moved round the sun in the curves 
called ellipses which, though resembling circles, differ 



72 Astronomy. 

from them in important respects. A method of drawing 
an ellipse is shown in fig. 20. Fix two pins at a and e 
into a sheet of paper on a drawing board. Let abp 
be a loop of thread put over the pins at a and b, and 
let p be the point of the pencil ; then if the point p 
be moved so as to keep the strings pa,pb, stretched, 
the point of the pencil will trace out the curve which 
is called an ellipse. 

It will be seen that ellipses may be of different 
shapes, thus if the pins remained the same as before, 
Fig. 20. an d if the length of the string 

which made the loop were a 
little greater, the ellipse which 
would be traced out by the 
point of the pencil would be 
less oblong, and would ap- 
proach more nearly to a circle ; 
on the other hand, if the length of the string were 
shorter the ellipse would become more oblong. 

The two points a and b of the ellipse are termed 
its foci. 

The first of the three discoveries which have im- 
mortalised the name of Kepler is thus stated. 

The path of a planet round the sun is an ellipse in 
one focus of which the centime of the sun is situated. 

Thus let s (fig. 21) represent the centre of the 
sun, then the ellipse abpq denotes the path of the 
planet. In the majority of cases the ellipse approaches 
very closely to a circle. In none of the principal 
planets is the deviation from a circle so great as it is 
represented in the figure, which has been designedly 
exaggerated. 





Kepler's Second Laiv. 73 

§ 58. .Kepler's Second Law.— In speaking of the 
apparently circular motion of the planets we also as- 
sumed that each planet moved uniformly in its orbit. 
When this assumption comes to be rigidly tested by 
accurate observations, it is also found to be not abso- 
lutely correct. The planet is found to be moving 
more rapidly at some parts FlG * 2I * 

of its path than at others. 
The law of these motions 
was also discovered by 
Kepler, and is expressed 
by his second law which is 
thus stated : — 

In the motion of a planet 
round the sun, the radius vector drawn from the centre 
of the sun to the planet sweeps over equal areas in equal 
times. 

Thus, for example, in fig. 21, when the planet 
moves from a to b, its radius vector sweeps out the 
area a s b, and in moving from p to q the radius 
vector sweeps out the area psq. Now Kepler's 
second law asserts that if the area a s b be equal to 
the area psq, then the time taken by the planet in 
moving from a to b is equal to the time taken by the 
planet in moving from p to q. 

We can now see how this will explain the varia- 
tions in the velocity with which the planet is moving, 
for since the planet has to move from p to Q in the 
same time as it takes to move from a to b, and since 
the distance p q is very much longer than the distance 
a b, it follows that the velocity of the planet must be 
greater when it is moving through p q than when it 



74 Astronomy. 

is moving through a b. We hence see that the planet 
when near the sun must be moving with greater ra- 
pidity than when it is at a distance from the sun. 

§ 59. Kepler's Third Law. — In the two laws of 
Kepler already discussed we have been considering 
the motion of only one planet. We have now to con- 
sider the remarkable law of Kepler which relates to a 
comparison between two planets. 

The squares of the periodic times of two planets have 
the same ratio as the cubes of their mean distances 
from the sun. 

To explain this we should first remark that by the 
mean distance of the planet from the sun is to be 
understood a length equal to one half that diameter of 
the ellipse (fig. 21) which passes through the two foci. 
We shall illustrate this law by a comparison between 
the cases of Venus and the earth. The periodic times 
of the. earth and Venus are respectively 365*3 days 
and 2247 days, while the mean distances are in the 
ratio of roooo to 07233. Now we have by an easy 
calculation 

fSfiaV- 2-643 

V2247/ 



and 



( 



iooo\ 3 , 

) =2-643 



,721 

which verifies the law. 

Kepler's three laws are found to be borne out com- 
pletely, even to their minutest details, when proper 
allowance has been made for every disturbing ele- 
ment. 



75 



CHAPTER XL 



THE LAW OF GRAVITATION. 



Fig. 22. 



§ 60. Gravitation of the Earth. — We have now to 
refer to the splendid discoveries made by Sir Isaac 
Newton, by which he was able to reveal the true 
cause of those movements of the planets which the 
laws of Kepler so faithfully expressed. It is impossi- 
ble in a book of this size to do more than glance at 
this subject, which embraces the most difficult pro- 
blems, in astronomy. 

Let abcd (fig. 22) represent a section 01 the 
earth, and suppose that a p, b q, c r, d s are towers 
erected at the correspond- 
ing spots. Now, if stones 
be let drop from the top of 
the towers at pqrs they 
will fall on the points 
abcd respectively. The 
four stones will move in 
the direction of the arrows. 
From p to a the stone 
moves in an opposite direc- 
tion to the motion from r 
to c, and from q to b it moves from right to left, 
while from s to d it moves from left to right. These 
movements are thus in different directions, but if we 
produce their directions as indicated by the dotted 
lines they all pass through the centre o. We are so 
accustomed to the falling of a body that it does not 




76 Astronomy. 

excite in us any astonishment, and rarely even pro- 
vokes our curiosity. A clap of thunder, which every 
one notices, though much less frequent is not really 
more remarkable. We all look with attention upon 
the attraction of a piece of iron by a magnet, and 
justly so, for the phenomenon is a very remarkable 
one, and yet the falling of a stone is produced by a 
far grander and more important force than the force 
of magnetism. 

We thus see that the earth must possess some 
power whereby it draws towards itself bodies situated 
near its surface. The ballast dropped from a balloon 
tells us that, even if we go to a great height, this power 
of drawing bodies towards itself still continues, nor 
does it require any great effort of the imagination to 
suppose that the earth would still continue to attract 
bodies towards it even though they w r ere at very stu- 
pendous distances from its surface. 

§ 6 1. Gravitation towards the Sun. — We can then 
conceive that the sun being a very great and massive 
body, vastly larger than the earth, may, like the earth, 
have the power of drawing bodies towards it, and we 
can show to a certain extent how this will explain the 
motions of the planets, though it is only possible for 
us here to give the merest outline of the subject. 

In the first place, it is known that if a body be 
once set in motion it will continue to move on for 
ever uniformly in a straight line unless a force act 
upon it. Now, a planet is not moving in a straight 
line, and therefore it is plain that some force must be 
continually acting upon the planet. The force in 
question undoubtedly is. the attraction of the sun. 



Law of Gravitation. 77 

The beginner will probably find some difficulty in 
understanding how if a planet were continually being 
attracted towards the sun it should, notwithstanding, 
continue to describe the same orbit for ever, and not 
ultimately fall into the sun. We proceed to explain 
this point. 

If a planet were originally at rest there can be no 
doubt that the attraction of the sun would tend to 
draw it in directly towards the sun, and that after a 
time the planet would fall into the sun. The case is, 
however, materially altered w T hen the planet is ori- 
ginally started with a velocity in a direction not point- 
ing exactly towards the sun. In this case the planet 
will never fall into the sun. 

§ 62, Illustration. — A stone which is simply 
dropped from the top of the tower pa (fig. 22) falls 
along the vertical line pa to the ground at a. If, 
however, instead of simply dropping the stone we 
throw it horizontally, then it is well known that the 
stone describes a curved path and falls on the ground 
at x. If it were not for the attraction of the earth, 
the stone thrown horizontally from p would move in 
the direction pz in which it was thrown ; thus we 
learn that the effect of the attraction has been to de- 
flect the stone from the straight line, in which it 
would otherwise have moved, and to make it move in 
a curved line. 

If the stone had been thrown from p with a greater 
velocity than in the case we have been considering, 
then the path which it takes may be represented by 
P y. The difference between the two curves p x and 
P Y is due entirely to the difference between the initial 



78 



Astronomy. 



Fig. 23. 



velocities of the stone. The attraction of the earth 
was, of course, the same in both cases. We thus see 
that the greater the initial velocity the smaller is the 
curvature of the path produced by the attracting force 
of the earth. 

§ 63. Explanation of the Motion of a Planet in 
a Circular Orbit. — We now proceed to explain how it 
is that a planet can continue to move for ever in an 
unaltered orbit, and though the orbits of the planets 
are not exactly circular, they are sufficiently nearly so 
to enable us for the sake of illustration to consider a 
hypothetical planet moving in a perfect circle of which 
the sun is the centre. 

Let s (fig. 23) represent the sun, and let t be the 
initial position of the planet. Let us now make 

different suppositions with 
respect to the initial state 
of the planet. In the first 
place, if the planet be simply 
released it will immediately 
begin to fall along t s into 
the sun. If we draw t z 
perpendicular to s t, and if 
we suppose that initially the 
planet was projected in the direction t z, the attraction 
of the sun at s will deflect the planet from the line tz 
which it would otherwise have followed, and compel 
it to move in a curved line. The particular curve 
which the planet will adopt depends upon the velo- 
city given to it along t z. With a small initial 
velocity it will follow the path t x, with a greater 
velocity the path t p, and with a greater still the path 

TY. 




Planetary Orbits. 79 

Let us now consider the effect which the attrac- 
tion of the sun will have upon the velocity of the 
planet. It is quite plain that if the planet had been 
originally projected directly towards s along the line 
T s, that the sun's attraction would tend to increase the 
initial velocity. It is equally plain that if the planet 
had been originally shot away from the sun along the 
line s t, that the effect of the sun's attraction would 
have been to diminish the velocity. But what would 
have been the effect upon the velocity in the interme- 
diate cases; let us consider them separately. When the 
planet moves along the curve t y it is at every instant 
after leaving t going further away from the sun. It is 
manifest that it is thus going against the sun's attrac- 
tion, and that therefore its velocity must be diminish- 
ing. On the other hand, when the planet is going 
along t x it is constantly getting nearer to the centre 
of the sun, and consequently its velocity must be 
increasing. It is therefore plain that for a path some- 
where between t x and t y the velocity of the planet 
must be unaltered by the sun's attraction. 

With centre s and radius s t describe a circle, and 
take p a point upon that circle exceedingly near to t. 
Now if we suppose that the planet be projected from 
t with a certain specific velocity it will describe the 
small arc t p. We can easily see that when the 
planet runs along this arc its velocity remains un- 
altered. The attraction of the sun always acts along 
the radius, and hence in describing the arc t p the 
planet has at every instant been moving perpendicu- 
larly to the sun's attraction. It is manifest that in 
such a case the sun's attraction cannot have altered 
the velocity, for it would be impossible to assign any 



80 Astronomy. 

reason why it should have accelerated the velocity 
which could not be rebutted by an equally valid 
reason why it should have retarded it. We thus 
see that the planet reaches p with an unchanged 
velocity, but at p the planet is precisely under the 
same circumstances as it was at the instant of its pro- 
jection ; it has the same velocity in each case, and it 
is in each case moving perpendicularly to the radius. 
It is therefore clear that after passing p the planet will 
again describe a small portion of the circle which will 
again be followed by another and so on ; i.e. the 
planet will continue to move in a circular orbit. 

What we have now shown amounts to this, that if 
a planet were originally projected with a certain 
specific velocity in a direction at right angles to the 
radius connecting the planet and the sun, that then 
the planet would continue for ever to describe a circle 
round the sun. 

It will not be difficult to imagine that if the con- 
ditions we have supposed be not rigorously fulfilled, 
that is, if the velocity be not exactly the correct one, 
t>r if the direction of projection be not exactly per- 
pendicular to the radius vector that then the orbit 
may still be a closed curve, not differing very widely 
from a circle. 

§ 64. Motion of a Planet in an Ellipse. — It can 
be proved by mathematical reasoning w T hich we do 
not attempt to explain here, that, when the force of 
attraction is such that it varies according to the inverse 
square of the distance, the curve which a planet pro- 
jected in any direction would describe must be, if not 
a circle or an ellipse, one or other, of the two remain- 



Orbits of Comets, 



81 



ing forms of the curves called conic sections, that is, 
it must be either an hyperbola or a parabola. 

§ 65. Motion of Comets. — All the planets move 
in ellipses but we have examples among the heavenly- 
bodies of motion in the two other curves. 

Comets are bodies which move around the sun 
under the influence of its attraction. Some comets 
describe ellipses of greater or less eccentricity. It 
more usually happens, however, that the path in 
which a comet moves is indistinguishable from a 
parabola. 

The shape of the parabola may be inferred from 
fig. 24. a b is a fixed straight line, and s is a fixed 
point. Now if a point F 

p move so that the 
distance p s is con- 
stantly equal to the 
length of the per- 
pendicular p q let 
fall from p upon the 
straight line a b, then 
the point p traces out 
the curve which is 
called a parabola. It 
can be shown that if 
we imagine one focus 
of an ellipse to re- 
main fixed while the 
other focus is moved away to an indefinitely great 
distance the ellipse will become modified into a para- 
bola. It is quite possible that a comet which appears 
to us to be moving in a parabolic curve round the sun 

G 




82 Astronomy. 

in the focus at s may often be moving in an ellipse 
which is so extremely long that the part of the orbit 
which we see near the sun is indistinguishable by 
our observations from an exact parabola. 



CHAPTER XII. 

PARALLAX. 



§ 66. Distance of the Moon from the Earth. — 

To obtain precise knowledge of the movements of the 
heavenly bodies, it is necessary for us to ascertain the 
distances by which they are separated from the earth. 
We proceed to explain the methods by which some 
of these distances have been determined. 

We shall, in the first place, consider the case of 
the moon, which is the nearest neighbour of the earth 
among the celestial bodies. It is very easy to observe 
that the moon moves round the earth once every 27*3 
days. As the apparent size of the moon remains 
nearly constant, it is obvious that the orbit of the 
moon cannot differ very widely from a circle. In fact, 
just as the earth moves round the sun in obedience to 
the attraction of the sun, so the moon moves round 
the earth in obedience to the attraction of the earth. 
It would, however, be hardly correct to speak of the 
orbit of the moon as an ellipse. That this orbit is not 
exactly an ellipse is not in any way inconsistent with 
the truth of the theory of gravitation ; it is, indeed, 






Moon's Distance from the Earth. S3 

rather a confirmation of this theory, for it can be 
shown that it is the attraction of the sun which de- 
ranges the motion of the moon from what it would be 
were this disturbing cause absent. When these dis- 
turbances are taken account of, the laws of gravitation 
are found to be fulfilled. 

Some of the other planets are, like the earth, 
attended by one or more moons or satellites ; but for 
a full account of the circumstances of each planet in 
this respect, reference must be made to some work on 
descriptive astronomy. 

To determine the distance of the moon from the 
earth, w r e require two observations of the moon made 
at places widely distant on the surface of the earth. 
We shall simplify the description of this operation as 
much as possible, for the purpose of presenting it in 
an elementary form. 

Let a and b (fig. 25) represent two stations on 
the earth, having the same longtitude, from which the 
moon is observed. Let c p be the polar axis of the 
earth. Now, we may suppose that the station b has 
been so chosen that at the instant of observation the 
moon m is situated in the zenith of the observer at b. 
We have now to remark that the fixed stars are at 
least some millions of times more distant from us than 
the moon. The stars are in fact so distant that the 
lines drawn from different points of the earth towards 
the same star are all practically parallel. Let us now 
suppose that the observer at b sees a star at s, which 
is just visible to him beside the edge of the moon, and 
that at this moment the observer at a directs his atten- 

G 2 



84 



Astronomy. 



tion to the same star, and observes its position relatively 
to the moon. The star is seen in the direction a s, 
which is parallel to b s, but the moon is seen from a 
in the direction a m, and, consequently, the observer 
at a sees the moon separated from the star by the 
angle mas. Now, by suitable instruments, the angle 
m a s can be carefully measured, and from this 
measurement the distance of the moon can be de- 
termined. 

Let us consider this triangle acm, The side a c 
is equal to the radius of the earth, which, for this pur- 
Fig pose, we may suppose to 

be a sphere. The angle 
a c b is the excess of the 
latitude of the station a 
over the latitude of the 
station b. This is, of 
course, known, because 
the stations are known. 
Also, since a s is parallel 
to b s, it follows that the 
angle a m c is equal to the 
angle mas, and therefore 
the angle a m c is known. 
In the triangle acm we 
therefore know one side, 
A c, and two angles. It follows that the triangle can be 
constructed to scale, and thus the length m c can be 
determined, or this length can be computed by the 
aid of trigonometry. 

The angle AMcis termed the moon's parallax. 
We have in the figure greatly exaggerated this angle. 




Transit of Venus. 85 

The distance of the moon from the earth, as deter- 
mined by these observations, is about sixty times the 
earth's radius. 

§ 67. Distance of the Sun from the Earth. — 
Owing to the comparative proximity of the moon to 
the earth, the determination of its distance is a much 
more simple problem than the determination of the 
distance of any of the other heavenly bodies. The 
scientific importance, however, of knowing the scale 
upon which the universe is built is so obvious that 
astronomers have paid a great deal of attention to the 
determination of the distance from the earth to the 
sun, which, as we shall presently see, is the standard 
of astronomical measurement. 

§ 68. The Transit of Venus.— There are several 
distinct methods by which this problem has been 
solved. The best known of these 
methods, even if not the most 
trustworthy, depends upon obser- 
vations of the phenomenon called 
the Transit of Venus, to which we 
have already referred. 

We shall endeavour to sim- 
plify the statement of this method 
by leaving out several of the de- 
tails which complicate its application in practice. 

The planet Venus on certain rare occasions comes 
between the earth and the sun, and is then seen by 
an observer upon the earth like a black spot upon the 
face of the sun. Thus, suppose the circle cab (fig. 26) 
to represent the apparent disk of the sun, the planet 
Venus appears to enter on the disk of the sun at a, 




86 Astronomy. 

and then moving across the sun in a direction which 
is indicated by the dotted line a b, leaves the sun at b. 
The time occupied in the passage of Venus across 
the sun may be about four hours. When Venus is 
just completely inside the sun, as shown in the figure, 
where the circle expressing the .edge of Venus just 
touches internally the circle expressing the edge of 
the sun, Venus is said to be at first internal contact. 
We shall now show how, by observing the time at 
which first internal contact takes place, the distance of 
the sun from the earth is to be determined. Let pqt 
(fig. 27) denote the sun, of which the centre is s. Let 

Fig. 27. 



A b denote the earth, and let x and y denote two posi- 
tions of the planet Venus. Suppose we draw a t a 
common tangent to the sun and the earth, and also 
the common tangent b t, touching the earth in B 
and the sun in a point so close to t as to be un- 
distinguishable therefrom. The circle through a b 
denotes the orbit of the earth ; and the circle through 



Transit of Venus. 87 

x y denotes the orbit of Venus, and the arrows in- 
dicate the directions in which the earth and Venus 
are moving. Now, as Venus is moving much faster 
than the earth, it follows that Venus will overtake 
the earth, and thus at a certain tin^e will arrive in 
the position x. (It will be seen that we are assum- 
ing for the present the orbits of the earth and Venus 
to lie in the same plane.) Now, what will be the ap- 
pearance of Venus when it is at x, as viewed from the 
station a on the earth ? The observer at a will just 
be able to see Venus at first internal contact, and 
having previously regulated his clock accurately, he 
will be able to note the moment at which Venus occu- 
pies the position x. 

We have already pointed out (§ 53) the artifice by 
which we may suppose the earth to be at rest in its 
orbit, while the movements of Venus relative to the 
earth remain unaltered. In fact, if the earth were 
at rest, and if the periodic time of Venus in its orbit 
were 584 days, then the appearances of Venus with 
reference to the sun, and as seen from the earth, 
would be the same as they actually are when the earth 
is moving round the sun in 365 days, and Venus in 
224 days. We shall then suppose that the earth is at 
rest in its orbit, and that Venus is moving with the 
slower motion just referred to. 

Let us now suppose that Venus moves on until it 
reaches the position y. To the observer at b Venus 
will now be visible at first internal contact. It is, 
therefore, clear that a is the spot on the earth at which 
the internal contact is first seen, and that B is the 
spot on the earth where the internal contact is last 



88 Astronomy. 

seen. A slight correction will have to be made here 
on account of the motion of revolution of the earth, 
upon its axis, for during the time occupied by Venus 
in passing from x to y the earth will have turned 
through an angle which is quite appreciable. Conse- 
quently the real point, b, on the earth's surface, where 
the internal contact is last seen, will be slightly dif- 
ferent from what it would have been if the earth had 
not rotated on its axis after the first internal contact 
had been observed from a. Astronomers, however, 
know how to allow for this difference, and we shall 
not here consider it further. 

We shall therefore suppose that expeditions are 
sent to the two stations a and b (of course as a matter 
of fact, they can only be sent to the places nearest 
A and b which are suitable from geographical consi- 
derations), and that at each of these two stations the 
moment of first internal contact is observed. We may 
also suppose that a telegraph wire is laid from a to b, 
so that at the instant of contact, as seen at a, a tele- 
graphic signal is despatched to b. The observer at b 
then notes the arrival of this signal on his clock, and 
when he himself sees the contact at a time also marked 
by his own clock, he is able with the greatest preci- 
sion to determine the interval of time between the two 
contacts. 

We have thus learned the time which Venus takes 
in passing from the position x to the position y. But 
we also know (§ 53) that the entire time which Venus 
requires for performing a revolution round the sun (re- 
latively to the earth) is 584 days ; hence if we assume 



Distance of the Sim from the Earth. 89 

that Venus moves uniformly, we can by a simple sum 
of proportion find the angle xsy. 

Now the radius t s is small compared with the 
distance s x. We may, therefore, with sufficient accu- 
racy for our present purpose suppose that the angle 
x t y is equal to the angle xsy. 

We may now consider the problem to be solved, for 
the distance a b being very nearly equal to the dia- 
meter of the earth is therefore known. Also the angle 
a t b is known, and therefore the distance a t from 
the sun to the earth is known. 

§ 69. Distance of the Sun from the Earth. — The 
most recent determinations make the sun's mean dis- 
tance from the earth equal to 

149,000,000 kilometres (92I- millions of miles). 

The actual distance, however, varies between 
147,000,000 kilometres in winter and 151,000,000 
kilometres in summer. 

By means of carefully executed measurements it is 
found that the average angle which the diameter of 
the sun subtends as seen from the earth is 1920". 

We are hence able to find the true diameter of 
the sun, for knowing the distance oa (fig. 2, § 2), 
and the angle a o b, we are enabled to find the dis- 
tance a b. The diameter of the sun as thus deter- 
mined is 

1,387,000 kilometres. 



90 Astronomy. 

CHAPTER XIII. 

PARALLAX OF THE FIXED STARS. 

§ 70. The Fixed Stars. — Great as is the distance 
of the sun from the earth, it is small compared with 
the distances of some of the fixed stars. It is true 
that we only know the distances of a very few of these 
bodies, but there is good reason to believe that the 
great majority of them are even more distant from us 
than those of which we do know the distance. 

It may be well for us here to glance for a moment 
at the rank which the fixed stars occupy among the 
other bodies which are found in the universe. Our 
sun is not only the source of light and heat to the 
planets, but it is also the centre around which they 
revolve, and its mass so overwhelmingly exceeds that 
of all the planets and their moons taken together that 
the planetary system is merely a minute adjunct to the 
sun. From a distance, less than the distance of any 
of the fixed stars, the planets would have become quite 
invisible though the sun might still be seen as a 
brilliant object. 

Astronomers are however 'led to the belief, that 
although the sun is to us on the earth vastly more im- 
portant than any of the other bodies in the universe, 
yet this imporcance is due rather to the comparative 
nearness of the sun to the earth than to the real 
pre-eminence of the sun among the other bodies of 
the universe. 

An examination of the countless myriads of those 



The Fixed Stars 91 

bodies with which the heaven is bespangled, and which, 
in order to distinguish them from the planets, we call 
the fixed stars, has taught us that, like our sun, they are 
bodies which shine by their own light and heat, and 
that their apparent minuteness is only due to the 
vast distances by which they are separated from us. 
When proper allowance has been made for the effect 
of this distance, it is found that some of these stars are, 
to say the least, as bright and large as our sun, and 
thus we are led to the conception that our sun is really 
only one of the host of stars which are so plentifully 
found even in the most remote regions of the heavens 
to which the power of the telescope can penetrate. 

We thus see that the measurement of the distance 
of a fixed star is an entirely different problem from 
the measurement of the distance of the sun. We were 
able in effecting this measurement to make use of the 
diameter of the earth as a base line. We shall how- 
ever find that a far larger base line is required for the 
celestial measurements now to be undertaken. 

§ 71. Annual Parallax of a Star. — We shall here 
only give an outline of the method which has been 
adopted by astronomers, for the actual application of 
the method, as in the case of the determination of the 
sun's distance, is complicated by a number of cir- 
cumstances which, though highly important for the 
astronomer, need not be entered upon in a work 
which aims merely at explaining the principles. 

It is easy to conceive that the apparent angular 
distance between a star and the centre of the sun can 
be measured by suitable observations. In fact if the 
right ascension and declination of the centre of the 



92 Astronomy. 

sun and the star be determined in the usual way, then 
the angle could be calculated by spherical trigonometry; 
or indeed, we might suppose the positions of the star 
and the sun to be plotted upon a globe, and the angle 
between the two positions measured in the usual way. 
Now, supposing this angle to have been measured at a 
suitable epoch of the year and the measurement to 
have been repeated precisely half a year afterwards, 
we should then have the means of rinding the distance 
of the star. 

For suppose (fig. 28) that s represents the position 
of the star, and a d b be the orbit of the earth ; then 
Fig z8 when the earth is at a, 

37 Y/ ,**& we measure the angle 

/ / //' sab. Six months after- 

wards, when the earth is 
at b, we can measure 
/' / / the angle s b a. The 

/ /' / / distance a b is double 

/ 1 / the distance of the sun 

from the earth, hence in 
v the triangle s a b we 
know the base a b, and 
the two base angles, and hence the triangle is deter- 
mined and the sides a s and b s are known. The 
angle which the radius of the earth's orbit subtends at 
a star is called the annual parallax of the star. 

§ 72. Impracticability of this Method.— The stars 
are, however, so excessively remote from us that the 
angle sap differs from the angle s b p by only an 
exceedingly minute quantity. This being so, a minute 
error in the measurement of one of the angles might 



*r 



Parallax of the Fixed Stars. 93 

cause a very large error in the distance of the star 
concluded from such measurement. Now there is 
one source of error which even the greatest care 
cannot entirely obviate, and that is the refraction 
of the atmosphere. It is true that we can calculate 
and allow for the grossest part of this error ; but even 
when this allowance has been made as well as our 
knowledge will permit, there are still outstanding small 
irregularities which would prevent the measurement 
of the angles being made with the required precision. 

§ 73. Determination of the Difference of the 
Parallax of two Stars. — We are therefore obliged to 
resort to a somewhat modified method. Suppose 
that there is another star which, on the celestial sphere, 
appears pretty close to s, but which is very much moie 
distant from us than s. Let ax and by (fig. 28) be 
lines drawn from A and B in the direction of this 
very distant star. Finally, we shall suppose that this 
auxiliary star is so exceedingly remote that the lines 
a x and B y are practically parallel. We now 
measure the angle x a s between the two stars when 
the earth is at a ; and then measure the angle ybs 
between the two stars when the earth is at B. Now 
it is true that both of these angles are also affected by 
refraction, but if the two stars are apparently very close 
together on the celestial sphere the effect of refraction on 
the relative positions of the two stars is insignificant. 
The apparent place of each star is of course slightly 
different from the real place on account of refraction, 
but the two stars being close together (on the celestial 
sphere) undergo very nearly equal displacements by 
refraction, and the small difference in the relative 



94 Astronomy. 

position and the angular distance, which refraction is 
able to produce, is susceptible of being computed 
with the utmost precision. 

We shall now show how these observations will 
enable us to compute the distance a s. Since ax is 
parallel to by, the angle yos is equal to the angle 
x a s, but the angle yos is equal to the sum of 
the angles osb and obs, and therefore the angle 
A s B is equal to the difference betw r een the angles 
xas and ybs. It follows that the angle a sb 
is determined by taking the difference between the 
two measurements of the angular distance of the stars 
corrected for refraction. 

The angle sab can then be measured, and even 
if a minute error in the determination of this angle 
should arise from the uncertainty of the refraction, it 
would produce an inappreciable effect upon the dis- 
tance required. We are therefore enabled, since a b is 
known, to construct the triangle sab, and thus the 
distance sa is determined. 

§ 74. The Proper Motion of the Stars.— To de- 
termine the distance of a fixed star by this method it 
is therefore necessary to have another star adjoining 
it on the celestial sphere, the distance of which is 
very much greater. The question here arises, how 
are we to know which of two apparently adjacent 
stars is farther off than the other ? There is really 
no way of making sure of this before the actual ob- 
servations have been made. There are, however, 
some d priori considerations which enable us to 
make a coarse guess as to whether a star is com- 
paratively near us. 



Proper Motion of the Stars. 95 

It is most probable, in fact it is practically certain, 
that every one of the stars is actually in motion. The 
relative places of the stars on the heavens are thus 
gradually changing. These changes, however, take 
place with such extreme slowness, that even in the 
lapse of centuries the forms of the constellations 
and the general appearance of the heavens have not 
appreciably altered. Even when the places of the 
stars have been determined with the utmost accuracy 
which meridian observations will permit, we do not 
find in the great majority of stars any perceptible 
change of position from one year to another. There 
are, however, a limited number of stars possessing 
an amount of proper motion (as it is called) which is 
quite appreciable in accurate observations. Now the 
fact of our seeing this proper motion and being able 
to measure it is a presumption that those stars which 
possess the proper motion are probably neaier to 
us than others in which no proper motion has been 
detected. This is the presumption which has chiefly 
guided those astronomers who have hitherto devoted 
their attention to the measurement of the distances of 
the stars from the earth. If, in the immediate vicinity 
of a star which has a large proper motion, a minute 
star be visible which has not that proper motion, it 
may be presumed that the former of these stars is 
nearer to us than the latter, and that the apparent 
contiguity of the two stars on the surface of the celes- 
tial sphere is only due to one of the stars lying near 
the line of sight directed towards the other. 

§ 75. Distances of the Stars. — The distances of 
several stars have been determined in this way. Of 



g6 Astronomy. 

these distances none are less than 200,000 times the 
distance of the earth from the sun. From so vast a 
distance as this the earth's orbit only appears about 
the same size as a silver quarter dollar would do at a 
distance of two and a half kilometres ! (\\ miles.) 



CHAPTER XIV. 

THE PRECESSION OF THE EQUINOXES. 

§ 76. Alterations in the Right Ascensions of Stars. 

■ — We have already explained the general method by 
which the right ascension of a star may be deter- 
mined (§ 23). Let us suppose that this operation is 
repeated for the same star at widely separated intervals 
of time ; to give deflniteness we state here the mean 
right ascension of Sirius at four different dates : 

Mean Right Ascension of Sirius. 





h 


m 


s 


Jan. 1, 1847 • 


. 6 


38 


25 


Jan. 1, 1857 . 


. 6 


38 


51 


Jan. 1, 1867 . 


. 6 


39 


17 


Jan. 1, 1877 . 


. 6 


39 


44 



We thus see that on the four dates here given, 
which are separated by intervals of ten years, the mean 
right ascensions of the star Sirius have perceptibly 
altered. It will also be observed that the changes in 
the right ascension take place uniformly at the rate of 
about 2*65 seconds of time per rnnum. In the course 



Precession of the Equinoxes. 97 

of centuries this change becomes very marked, even 
to the coarsest methods of observing, and conse- 
quently we find that this phenomenon was known to 
the ancient astronomers. 

§ 77. Precession of the Equinoxes. — Now let us 
state exactly what the phenomenon is. On January 
1, 1847, the vernal equinox crossed the meridian 
6 h 38™ 25 s before the star Sirius. On January 1. 
1877, the vernal equinox crossed the meridian 6 h 39^ 
44 s before Sirius. It is therefore obvious that the 
vernal equinox and Sirius are further apart now than 
they were thirty years ago. Compared with Sirius the 
vernal equinox now comes on the meridian a little 
earlier than it did thirty years ago, and thus the phe- 
nomenon in question has come to be known as the 
* Precession of the Equinoxes/ 

We have selected the star Sirius merely as an 
example ; had any star been chosen we should have 
equally found that relatively to that star the vernal 
equinox was continually changing its position. 

§ 78. The Ecliptic is at rest. — We are thus led to 
the belief that the positions of the equinoxes on 
the celestial sphere are in a state of continual change. 
Now as the equinoxes are the intersections of the 
ecliptic and the equator, it follows that one if not 
both of these circles must be continually changing its 
place upon the surface of the heavens. 

It is, however, easy to show that of these two 
circles the ecliptic at all events has no perceptible 
motion. If we could see the stars surrounding the 
sun in the heavens, we should find, for example, that 
every 23rd of May the sun passed between the 

H 



98 Astronomy. 

Pleiades and Hyades, that every 21st of August it 
passed exceedingly close to Regulus (a Leonis), and 
that on every 15th of October it passed a little above 
Spica (a Virginis). The track of the sun among 
the stars is thus invariable, and hence to account for 
the motion of the vernal equinox we must suppose 
that the ecliptic is at rest and that the equator is in 
motion. 

§ 79. Motion of the Celestial Pole. — By observa- 
tions of a star at widely separated intervals it has been 
found that the polar distance is changing, as well as the 
right ascension. Thus for the dates already given we 
have for the polar distances of Sirius : — 

Date. Mean Polar Distance of Sirius. 



Jan. 1, 1847 


. 106 


30' 


37" 


,, 1857 . 


. 106 


3i' 


24" 


„ 1867 . 


. 106 


32' 


11" 


„ 1877 . 


. 106 


32' 


56" 



We thus see that the angular distance from Sirius 
to the north pole is steadily increasing at the rate of 
about 4 //# 6 annually. It follows that either the north: 
pole or Sirius must be in motion on the surface of the 
heavens. If we make the same observations for any 
other star we find a similar change, and hence we see 
that there is a relative motion between every star in 
the heavens and the north pole. Now, shall we say 
that the stars are moving relatively to the pole, or the 
pole moving relatively to the stars ? If we reflect 
that the stars have next to no relative motion among 
themselves, it is obviously more natural for us to 



Precession of the Equinoxes. 99 

suppose that the pole is actually moving among the 
stars. 

To this conclusion also the observations of the 
changes in right ascension would have conducted us, 
for if the equator be in motion among the stars (as 
we have seen it is), then it is a necessary conse- 
quence that the pole, which is merely the point on 
the celestial sphere 90 from the equator, must be in 
motion also. 

We are thus led to inquire into the nature of the 
motion of the pole which will be adequate for the 
purpose of explaining the changes of right ascension 
and declination of the heavenly bodies to which we 
have adverted. 

§ 80. The Obliquity of the Ecliptic.— The first 
point to be considered is the inclination of the ecliptic 
to the equator. To determine the obliquity of the 
ecliptic, as this inclination is called, it is only neces- 
sary to observe the greatest declination of the sun on 
Midsummer-day, and this declination is the required 
obliquity. We shall here give the obliquity of the 
ecliptic as determined by this method in the years 
already referred to* 



Date. 


Obliquity of Ecliptic. 


June 21, 1847 . 


. 23° 27' 23 // «56 


1857 . 


• 23 27' 37''i2 


„ 1867 . 


. 23 27' i 3 "-8 5 


„ 1877 . 


. 23 27' 26 /,, 5i 



Now, though it would not be correct to say that the 
obliquity was absolutely constant, yet the changes in 

h 2 



IOO Astronomy. 

its value are extremely small In fact the mean of the 
four values just given is 

23 27' 25"*26 

and the difference between this quantity and the 
greatest or least of the four observed values is only 
about one seven thousandth part of the total amount. 

§ 81. Motion of the Pole among the Stars. — We 
are thus led to the conclusion that whatever be the 
motion of the equator among the stars it constantly 
preserves the same inclination to the ecliptic. 

Let p denote the pole of the celestial equator, and 
let t denote the pole of the ecliptic. Then, since the 
ecliptic remains fixed among the stars it follows that 
the place of t among the stars does not change. 
Now, since the angle between two planes is equal to 
the angle between the perpendiculars to those planes 
drawn through a point upon the line of intersection, it 
is evident that the obliquity of the ecliptic is equal 
to the angular distance of the poles p and t. Hence, 
since we have seen that the obliquity of the ecliptic 
remains constant, it follows that the arc p t must re- 
main constant, and that therefore p can only move in 
a small circle on the celestial sphere of which t is the 
pole. 

We have now only to ascertain the velocity with 
which p moves round in its small circle. 

By a comparison of ancient observations with 
modern observations the rate at which this motion is 
performed has been determined with great accuracy. 
It is found that the arc t p sweeps through an 
angle of 5o r/, 26 annually, and from this it is easy to 



Precession of the Equinoxes. 101 

calculate that, for p to complete a whole revolution 
round t, a period of nearly 26,000 years is necessary. 

The consequences of this continual change in the 
position of the pole are very remarkable. The polar 
star, at present of such importance to astronomers, 
was not always so near the pole as to be convenient 
for the many purposes to which it is now applied. 
Thirteen thousand years ago it was distant from the 
pole by more than 40 , and in thirteen thousand 
years more it will again be separated by the same 
distance. 

§ 82. The Pole of the Earth.— It should be 
observed that although the pole in the heavens is 
moving about among the stars in the way we have 
described, yet that the axis about which the earth 
rotates appears to be rigidly fixed in the earth. In 
fact (so far as observations have hitherto gone), we 
might suppose a rigid axis driven through the earth, 
and the earth to be spinning round this axis once in 
every sidereal day. This axis (of course carrying the 
earth with it) traces out a right circular cone, of which 
a perpendicular to the plane of the ecliptic is the axis, 
and the time occupied in the description of this cone 
is 26,000 years. 

It can be shown from dynamical principles that the 
actual pole of the earth might be revolving on the 
earth itself in a small circle in a period of 306 days; 
or to put the matter more plainly, if a line were 
drawn from the centre of the earth to the celestial 
pole, and if the point in which this cuts the surface of 
the earth were marked each day by a peg, then the 
positions of the pegs might not always be the same; 



102 



Astronomy. 



but all the pegs might lie upon a circle, such that the 
peg corresponding to the 307th day would be in the 
same place as that belonging to the first day. Obser- 
vations have been specially directed to this point, and 
it has been shown that even if such a motion of the 
pole on the earth exists, the circle which it describes 
can hardly be a dozen metres in diameter. 

§ 83. Permanency of an Axis of Rotation. — We 
shall now consider the mechanical cause of this 
very remarkable phenomenon. If a body (of the same 
shape as the earth) be set spinning about its polar 
axis, then the body will continue for ever to spin 
about this axis, and the direction of the axis will con- 
tinue for ever parallel to itself. In fig. 29 let pq 

represent the axis about 
which the earth is spin- 
ning, then, by the sym- 
metry of the figure it is 
obvious that the centri- 
fugal forces on all the 
parts of the earth will 
neutralise each other. 
If, however, from any 
cause the position of 
the earth be slightly deranged so that it occupies the 
place indicated by the dotted lines, then the cen- 
trifugal force acting upon the protuberant portions 
wiil have the effect of making the axis slowly revolve 
around its original position. It follows that the motion 
of the earth is stable when spinning about its polar axis. 
In the annual path of the earth around the sun, 
the axis of the earth (subject only to the small 




Precession of the Equinoxes. 103 

effect of precession) remains constantly parallel to 
itself. A familiar illustration of the same permanency 
of an axis of rotation is presented by the humming top, 
which will stand up straight when it is spinning, though 
it will not do so when at rest. 

§ 84. Cause of the Precession of the Equinoxes. 
There is however a disturbing cause in action which 
deranges the motion of the earth around its axis from 
the simple character it would otherwise have. This 
disturbing cause is due to the attraction of the sun 
and the moon upon the protuberant portions at the 
earth's equator. 

To explain this, we have to make use of a theo- 
rem in mechanics which we cannot demonstrate in 
this volume, but the truth of which will perhaps be 
admitted. If the earth be rotating round its polar 
axis, then that rotation will not be disturbed by any 
force which passes through the centre of gravity of the 
earth. In fact, so far as the mere rotation of the 
earth upon its axis is concerned, we might regard the 
centre of gravity as a fixed point, and then the force 
which passed through the centre of gravity could be 
neutralised by the reaction of the fixed point. 

Now if the earth were a perfect homogeneous 
sphere, the attraction of the sun or the moon would 
be a force passing through the centre of the sphere, 
and so would leave the rotation unaffected. Or, 
even if the earth were not a perfect sphere, or not 
homogeneous, still if the attracting body were so far 
off that all points of the earth might be considered as 
practically at the same distance from the attracting 
body, in this case also the attraction would be a force 



104 Astronomy. 

passing through the centre of gravity of the earth. 
The sun and the moon, however, are both so com- 
paratively near the earth that we are not entitled to 
make this supposition, and, consequently, neither the 
attraction of the sun nor of the moon passes through 
the earth's centre. To this is due the phenomenon of 
the Precession of the Equinoxes. 

Let p q (fig. 30) represent the axis of the earth, 
and let s be the position of the attracting body. Then, 
since the attraction varies inversely as the square of 
the distance, it follows that the portion of the earth 
turned towards the attracting body will be acted upon 

Fig. 30. 



^g 



by a greater force than the portion on the remote side, 
and, consequently, the total attraction will be directed 
along the line h s, which passes above the centre of 
^gravity of the earth c. Let h t represent the magni- 
tude of this force, both in intensity and in direction. 
Through the centre c draw a line x y parallel to h t, 
and let us suppose that equal and opposite forces c x 
and c y are applied at the centre c, each of these 
forces being equal to h t. The force c y may now be 
left out of view, for as it acts through the centre of 
gravity, it can have no effect upon the rotation of the 
earth around its axis. Thus the effect of the attracting 



Precession of the Equinoxes, 



105 



body upon the earth may, so far as the rotation of the 
earth is concerned, be represented by the pair of 
equal parallel and opposite forces h t and c x. Such 
a pair form what is known in mechanics as a couple. 

It would seem as if the immediate effect of this 
couple would be to turn the earth so as to bring its 
polar axis c p perpendicular to the line c s, or (sup- 
posing the sun to be the attracting body under con- 
sideration) to bring the plane of the equator to coincide 
with the plane of the ecliptic. The effect of the couple 
is, however, so entirely modified by the fact that the 
earth is in a state of rapid rotation, that paradoxical as 
it may appear, the real effect of the couple is not to 
move c p in the plane of the paper, but to make c p 
move perpendicularly to the plane of the paper. 

§ 85. Illustration of the Pegtop.— In explanation 
of this apparent paradox, we may remark that in a 
miniature form every schoolboy 
is already acquainted with a pre- 
cisely analogous phenomenon in 
the motion of a common pegtop. 
In fig. 3 1 the line p z is vertical, 
p c is the axis of the pegtop, and 
c is the centre of gravity of the 
pegtop. Now, if the pegtop when 
not spinning were placed in the 
position represented in the figure, 
the force of gravity acting along 
c h would immediately cause it to 
tumble over, the line c p moving in the plane of the 
paper. But when the pegtop is in a state of very 
rapid rotation, the circumstances are entirely different. 



Fig. 31. 




106 Astronomy. 

Every one has observed that the axis c P, so far from 
falling in the plane of the paper, commences to move 
perpendicularly to the plane of the paper, and will, in 
fact, describe a right circular cone around p z as an 
axis. It is undoubtedly true that after a time the 
angle zpc begins to increase, and that before long 
the pegtop really does tumble down, but this is solely 
due to the influence of disturbing forces, viz. friction 
at the point and the resistance of the air, and that if 
these forces could be evaded, the speed with which 
the pegtop spins would be undiminished ; and so 
long as that speed remained unaltered, so long would 
the axis of the pegtop continue to describe the right 
circular cone around the line p z. 

Assuming that what holds good in the case of the 
pegtop holds good in the colossal case of the earth 
itself, we should expect to find that the axis p c, in- 
stead of moving towards s and thus diminishing the 
obliquity of the ecliptic, would move perpendicularly 
to the plane of the paper and thus not alter the obli- 
quity of the ecliptic at all. The axis of the earth 
would then describe a right circular cone of which the 
axis is perpendicular to the plane of the ecliptic, and 
this is actually the motion which the precession of 
the equinoxes requires. 

§ 86. Precession due to both Sun and Moon. — 
The precession of the equinoxes is due to the action 
of both the sun and the moon. Owing, however, to 
the proximity of the moon its effect is greater than 
that of the sun. In fact of the total amount, about 
one-third is due to the sun and the remainder to the 
moon. 



io7 



CHAPTER XV. 

THE ABERRATION OF LIGHT. 

§ 87. Th3 Aberration of Light.— The discovery 
of the aberration of light, by Bradley, is one of the 
most interesting episodes in the history of science. 
In the hope of detecting the existence of annual pa- 
rallax in the star y Draconis, Bradley had observed 
the zenith distance of the star on all available oppor- 
tunities for an entire year. These observations re- 
vealed an apparent movement in the star, entirely 
different from the movement which would be produced 
by the annual parallax for which Bradley was in 
search. It was not until after this apparent motion 
had been detected and examined in several stars, that 
Bradley was enabled by a happy conjecture to give it a 
satisfactory explanation. Bradley found that the ap- 
parent movements of the stars which he had discovered 
were an immediate consequence of the fact that the 
velocity with which light travels, though exceedingly 
great, is still not incomparably greater than the velo- 
city with which the earth moves in its orbit round the 
sun. The phenomenon thus revealed is called the 
aberration of light. This discovery, though it relates 
to magnitudes so exceedingly small as to be per- 
ceptible only in very accurate measurements, is yet 
of so delicate and so beautiful a character that it 
must undoubtedly rank among the very greatest dis- 
coveries which have yet been made in astronomy. 



io8 



Astronomy. 



§ 88. Explanation of the Aberration of Light — 

Let s, fig. 32, represent a star to which a telescope 
is to be directed. If the telescope be at rest, it is 
obvious that the telescope should be pointed along 
the ray x s which comes from the star. If, however, 
the telescope be in motion a little consideration will 
show us that, when the star is seen, the telescope must 
generally not be pointed exactly at the star but in a 
somewhat different direction. Let us suppose that 
the telescope will move from the 
position marked a b to the position 
x y in the same time as the light 
from the star travels from b to x. 
Then it is plain that, for us to see 
the star, the telescope must be 
pointed in the way shown in the 
figure. For the star can only be 
seen when rays of light from the 
star enter the eye of the observer. 
The telescope must therefore be 
so placed that the rays which 
enter the object glass of the tele- 
scope can come out of the eye piece. When the 
telescope is in the position A b the light enters the 
telescope through the object glass at b; the motion of 
the telescope is then sufficient to enable the light to 
pass down the tube of the telescope without being 
lost against the sides, and when the telescope reaches 
the position x y the light emerges from the eye piece 
at x, and enters the eye of the observer. 

If, therefore, the observer, who, of course, shares 
the same motion as the telescope, observes the po- 




Aberration of Light. 109 

sition of the star, he will see the star in the direction 
x y in which the telescope is pointed, and. therefore, 
he will judge erroneously of the position of the star to 
an extent which is measured by the angle between the 
direction s x of the rays which come from the star and 
the direction x y in which the telescope is pointed. 

§ 89. Determination of the Velocity of Light. — 
It is an exceedingly interesting consequence of the 
discovery of the aberration of light that we are enabled 
to deduce from astronomical observations the velocky 
with which light travels through space. The move- 
ment of the telescope to which we have referred arises 
from the annual motion of the earth around the sun. 
This annual motion takes place at the average rate of 
29 kilometres per second, and consequently, 29 kilo- 
metres per second is the velocity with which the 
telescope is carried along. Now it is evident that 
while the telescope is carried over the distance ax, 
the light must travel through the distance bx, and 
hence we see that the velocity of the earth is to the 
velocity of light in the ratio which a x bears to bx. 
If, therefore, we could in any way find the angles of 
the triangle b a x, we should know the ratio which the 
velocity of light bears to the velocity of the earth in 
its orbit, and as the latter is known, the velocity of 
light would be determined. 

Of these, the angle bax is immediately known ; 
for as the earth is moving in the ecliptic (for the 
present wc may suppose the orbit to be circular) and 
in a direction perpendicular to the line drawn from 
earth to the sun, the earth must at any moment be 
moving towards that point on the ecliptic which is 90 



no 



Astronomy. 



from the sun. Therefore the point in the heavens 
towards which the earth is moving on any given day- 
is determined. The line ax, which indicates the 
direction of the motion of the telescope, is therefore 
directed to a point upon the heavens which is known. 
The angle bax is therefore known, for it is merely 
the angular distance between the point in the heavens 
to which the telescope is pointing, and the point on 
the ecliptic which is 90 from the sun. 

The angle a h x can also be determined by means 
of observations, and to show the principle of the 
method by which this is obtained we shall suppose a 
very simple case. 

Let c (fig. 33) represent the sun, and p the position 
of the earth in its orbit. Let p q be the direction of 
the telescope, which is pointed 
precisely to that point of the 
heavens towards which the 
earth is moving and which is, of 
course, a point on the ecliptic 
90 from the sun. Let us sup- 
pose that there is a star, situ- 
ated in the direction indicated 
by the line p s. In a quarter 
of a year after the earth was 
at p it will have reached the 
position a, and the telescope 
is again pointed to the same 
star. Now if it were not for . aberration the star 
would be seen in that point of the ecliptic which was 
180 from the sun, along the direction cb. Owing, 
however, to aberration, the telescope must be pointed 



Fig. 33. 




Aberration of Light. in 

in a somewhat different direction, a b. It follows 
that the angle cba will be equal to the difference be- 
tween 180 and the angle which the star makes with 
the sun, and hence the angle cba is known. This 
angle c b a is the difference between the real direction 
of the star and the direction in which the telescope is 
pointed. Of course, it will not generally happen that 
a star will be so opportunely situated as in the case 
we have supposed ; but the illustration will serve to 
exemplify the statement, that by suitable observations 
at different seasons of the year the angle abx (fig. 32) 
between the real and apparent direction of the star 
can be determined. Thus two angles of the triangle 
b a x are known, and thus the species of the triangle 
is known, and the velocity of light can be determined. 
§ 90. Other Determinations of the Velocity oi 
Light. — Another method by which the velocity oi 
light may be determined, and which is indeed the way 
in which that velocity was first discovered, is presented 
by the phenomena of Jupiter's satellites, J he planet 
Jupiter is attended by a very beautiful system of four 
moons. These moons are constantly being eclipsed 
by passing into the shadow of Jupiter. To see these 
eclipses only a small telescope is required, and they 
have consequently been much observed ever since the 
first discovery of the satellites of Jupiter by Galileo. 
From these observations the movements of the satel- 
lites have become so well known that it is possible to 
predict the occurrence of the eclipses, and the times 
at which they will commence and terminate. After 
many comparisons between these predictions and the 
actual observations certain discrepancies were brought 



112 Astronomy. 

to light, the cause of which was not at first manifest. It 
was, however, noticed that the eclipses occurred earlier 
than was expected when the earth was in that part of 
its orbit near Jupiter, and later than was expected when 
the earth was distant from Jupiter. This suggested 
the explanation that the velocity of light was not in- 
definitely great, and that thus, when we were near to 
Jupiter, we received tidings of the occurrence of an 
eclipse with less delay than when we were further off. 

The velocity of light has also been determined by 
means of actual experiments on the earth, and the 
results of these experiments agree in a remarkable way 
with the results deduced from aberration, and from 
the eclipses of Jupiter's satellites. 

Recent elaborate researches indicate that the velo- 
city of light is between 298,000 and 300,400 kilometres 
per second. 



CHAPTER XVI. 

THE SEASONS. 



§ 91. Changes of the Seasons. — Let fig. 34 re- 
present the path of the earth around the sun. We 
do not attempt in this figure to represent the earth 
and the sun to scale. Let n s be the direction of the 
axis about which the earth rotates, then in each of the 
four positions in which the earth is shown the direction 
n s will be parallel. 

Let us first consider the earth in the position & 
The north pole of the earth at n will then be turned 



The Seasons. I 1 3 

towards the sun, and consequently at or near the 
north pole there will be continual daylight. This is 
shown a little more fully in fig. 35 (p. 114). All 
the region inside the small circle e d (fig. 35) will be 
in constant daylight because the revolution of the 
earth about the axis n s cannot bring a place within 
this circle into the dark hemisphere. This circle, e d y 
is called the Arctic Circle, and it will thus be seen 



that during the Arctic summer all places within the 
Arctic Circle enjoy perpetual day. 

If the centre of the earth be joined to the centre 
of the sun, the joining line will cut the surface of the 
earth in the point c (fig. 35). The circle cv will also 
be of importance. When the earth has the position 
shown in the figure, the sun will be vertically over head 
at the point c. This circle is called the tropic of 
Cancer, and the sun can never be vertically overhead 
in any place which lies north of the tropic of Cancer. 

I 



114 Astronomy. 

Let us now draw a plane through the centre of 
the earth perpendicular to the polar axis n s. This 
plane will cut the surface of the earth in a circle, eq, 
which is called the equator. Since half this circle 
will lie in the illuminated hemisphere and half in the 
dark hemisphere, it follows that the day and night at 
the equator will be of equal length. At all places 
between the equator and the Arctic Circle there will 
be both daylight and darkness in every revolution of 
the earth, but as the portion of the earth which lies 
between these boundaries is more in the illuminated 
hemisphere than in the dark hemisphere, it follows 

Fig. 35. 





that the day will be longer than the night. On the 
southern hemisphere of the earth, i.e. the hemisphere 
between the south pole and the equator, we draw 
the circles/^ and gp precisely similar to the Arctic 
Circle and the tropic of Cancer in the northern ; these 
circles are called respectively the Antarctic Circle and 
the tropic of Capricorn. At any place between the 
equator and Antarctic Circle the night is longer than 
the day, while at any place between the Antarctic 
Circle and the south pole there is perpetual night. 

We have thus described the way in which the 
sun's light and heat are received by the different regions 
of the earth when the earth is in that part of its orbit 



The Seasons. 1 1 5 

denoted by c (fig. 34). Let us now see how this cor- 
responds to the seasons. 

Suppose the earth and sun to occupy the relative 
positions shown in fig. 35, then, as we have seen, 
the sun shines continually in the Arctic regions, 
while in the Antarctic regions the sun is not seen at 
all. Hence we have summer in the Arctic regions 
and winter in the Antarctic regions. Between the 
equator and the Arctic Circle the day is longer than 
the night, while between the equator and the Antarctic 
Circle the night is longer than the day. The warmth 
received from the sun is also very much greater in the 
northern hemisphere than in the southern hemisphere. 
The reason of this is that the sun shines much more 
perpendicularly on the earth between e and d than 
it does between e and f. Thus, throughout the 
whole of the northern hemisphere we have summer, 
and throughout the whole of the southern hemisphere 
we have winter. 

Let us now suppose the case when the earth is in 
the position of fig. 36. The condition of the two 

Fig. 36. 





hemispheres is reversed. The Arctic Circle is in per- 
petual darkness, the Antarctic Circle is in perpetual 
sunshine. Winter reigns over the entire northern 

1.2 



n6 



Astronomy. 



hemisphere, while summer prevails throughout the 
southern hemisphere. 

Finally, when the earth is at the intermediate 
positions we have the condition of spring or autumn, 
for now, as we see by fig. 37, the axis of the earth is 
perpendicular to the line joining the centre of the 
earth to the sun. Hence it is evident that, in this 

Fig. 37. 





case, day and night are of equal length all over the 
globe. We thus see that by the revolution of the 
earth about the sun, combined with the rotation of 
the earth about its axis and the constant inclination 
of the earth's axis to the plane of the ecliptic, the 
changes of the seasons are produced. 



CHAPTER XVII. 

THE SOLAR SYSTEM. 

§ 92. The Solar System. — By the expression solar 
system we are to understand the group of celestial 
bodies which consists of the sun himself, the planets 
and their satellites, and the comets. To these should, 
perhaps, be added a vast host of minute bodies which, 



The Solar System. 



117 



when they come into our atmosphere, produce the 
well-known phenomena of the shooting stars. 

All the bodies we have mentioned form one iso- 
lated group in the universe. The most prominent 
member of the group is, of course, the sun, which far 
exceeds in dimensions all the other bodies of the solar 
system taken together. 

In fig. 38 we give a general sketch of the relations 



Fig. 38. 




of the different members of the solar system. It is, 
however, not possible to represent conveniently in a 
figure the real proportions of the orbits. 



Il8 Astronomy. 

§ 93. The Planets. — Tn the centre we have the 
sun, round which all the other bodies circulate. The 
planet, so far as we know at present, which is nearest 
to the sun is Mercury, to the motions of which we 
have already referred (§ 54). Mercury is so extremely 
close to the sun that the intensity of the radiation of 
heat from the sun must be seven times greater on 
Mercury than on the earth. The diameter of Mer- 
cury is somewhat less than half the diameter of the 
earth. 

Next in order comes Venus (§ 46) which is about 
the same size as the earth. Then proceeding outwards 
from the sun comes the earth, and this is succeeded 
by Mars, of which the diameter is only about half 
that of the earth. The earth is accompanied by 
one moon, and Mars by two very small moons. 

Next in order to these four planets come the vast 
group of minor planets which are called asteroids. 
Of these nearly two hundred have been already dis- 
covered. They are all, with possibly one or two ex- 
ceptions, invisible to the naked eye ; the diameters 
of most of them are probably only a few kilometres. 
The discovery of these planets, of which the first 
was discovered on the first day of this century, has 
given rise to an entirely new department of astro- 
nomy. 

Outside the group of asteroids come the colossal 
members of the system of planets. The nearest of 
these to the sun is the planet Jupiter, which is 
much the largest of all. The diameter of Jupiter is 
more than ten times as great as the diameter of the 
earth, while the diameter of the orbit in which 



The Planets. 119 

Jupiter moves around the sun is five times the dia- 
meter of the orbit of the earth. 

The time occupied by Jupiter in completing one 
revolution about the sun is about twelve years. Not- 
withstanding the vast size of Jupiter his rotation upon 
his axis is performed more rapidly than the corre- 
sponding rotation of the earth, the period being 
scarcely ten hours. Jupiter is attended by no less 
than four moons or satellites. The nearest of these 
moons to Jupiter is only distant from him by six 
times his radius. This satellite moves completely 
round Jupiter in less than two days. The fourth or the 
most distant satellite is about four or five times as far 
from Jupiter as the first satellite, and its time of revo- 
tion is about sixteen days. 

We may thus contrast the circumstances of the 
satellites of Jupiter with the circumstances of our own 
satellite. The moon is distant from us by about sixty 
times the earth's radius, and the time of its revolution 
is about 27*3 days. We thus see that our moon is re- 
latively much more distant from us than any of Ju- 
piter's satellites are from him. There is also another 
very remarkable point of contrast, for while the mass 
of the moon is about one ninetieth part of the mass 
of the earth, the largest satellite of Jupiter (the 
third) is scarcely a ten-thousandth part of the mass of 
Jupiter. 

Next in distance from the sun comes Saturn. 
This superb planet, which is second only to Jupiter in 
size, is in some respects the most remarkable object 
in the solar system. In addition to a retinue of nc 
less than eight satellites, Saturn is attended by a ring 



120 Astronomy. 

or rather series of rings, which is probably without a 
parallel in the solar system. 

Next after Saturn comes the much fainter object 
Uranus. This, though a keen eye may see it without 
a telescope, was not recognised as a planet before Sir 
William Herschel's discovery of it in 1 781. Four satel- 
lites revolve around it, two of which were discovered 
by Herschelin 1787 and two by Mr. Lassell in 1847. 
These satellites are remarkable for their revolution in 
orbits nearly perpendicular to the plane of the orbit 
of the planet. 

The outermost known planet of our system is called 
Neptune. This planet is attended by one satellite. 

Figure 38 also shows a portion of the parabolic 
orbit of a comet. 



CHAPTER XVIII. 

THE FIXED STARS. 



§ 94. Magnitudes of the Stars.— On a clear night 
the heaven is seen to be bespangled with a vast mul- 
titude of minute points of light. Astronomers are in 
the habit of calling these objects the fixed stars, for 
the purpose of distinguishing them from the planets. 
The fixed stars maintain their relative positions un- 
changed from year to year, while the positions of the 
planets are (as we have seen) incessantly changing. 
It is, however, to be observed that the planets which 
can be easily seen with the unaided eye are only 
five in number (viz. Mercury, Venus, Mars, Jupiter, 



The Fixed Stars. 121 

Saturn). Uranus can be seen like a very faint star, 
and one or two of the remaining planets have occa- 
sionally been detected by sharp vision. It is thus 
evident that out of the multitude of celestial objects 
visible to the unaided eye every clear night by far 
the largest part consists of what we call the fixed 
stars. 

The first feature connected with the stars to which 
we shall direct attention is their very different degrees 
of brightness. Astronomers have divided the stars 
into different groups corresponding to their bright- 
ness. Thus, about twenty of the brightest stars are 
said to be of the first magnitude. Among these we 
may mention Sirius (the brightest star in the heavens), 
Vega, Capella, Aldebaran, Rigel, Arcturus, Spica, and 
Betelgueze. 

Next in order to these come the stars of the second 
magnitude. Of these we may mention as examples 
the four brightest stars in the constellation of Ursa 
Major (the Great Bear). 

§ 95. Numbers of the Stars. — Argelander has 
computed the number of stars of each of the different 
magnitudes with the results, here given. 



1st 20 


4th 425 


7th 


13,000 


2nd 65 


5th 1,100 


8th 


40,000 


3rd 190 


6th 3,200 


9th. 


142,000 



It will thus be noticed that the numbers of the 
stars of each magnitude increase with very great 
rapidity as the brightness diminishes. Thus, though 
there are but twenty stars of the first magnitude, there 
are 142,000 stars of the ninth magnitude. 



122 Astronomy. 

Of these stars, however, only a comparatively small 
number are visible to the unaided eye ; the smaller 
stars of the 6th magnitude are so faint that only the 
best eyes can see them, while no one can perceive stars 
of the 7th magnitude without a telescope. The num- 
ber of stars which can be seen with the unaided eye 
in our latitudes may be estimated as about 3,000. 

It is hardly possible to estimate the numbers of 
stars whose magnitudes are lower than the 9th. 
This partly arises from their prodigious numbers, and 
partly from some uncertainty in the estimation of these 
magnitudes. Argelander has, however, published a 
series of maps of the stars in the Northern Hemis- 
phere. These maps include all stars from the brightest 
down to a magnitude intermediate between the 9th 
and the 10th, and upwards of 300,000 stars are re- 
corded upon these maps. The still smaller stars are 
as yet uncounted. In fact, every increase in telescopic 
power serves to render visible countless myriads of 
stars which an inferior power would not show at all. 

§ 96. The Milky Way. — The prodigious richness 
of the heavens in the smaller classes of stars is well 
illustrated by the nature of the Milky Way. The 
Milky Way is an irregular band of faint luminosity, 
which encircles the whole heavens. The telescope 
shows that this faint luminosity really arises from 
myriads of minute stars, which, though individually so 
faint as to be invisible to the naked eye, yet by their 
countless numbers, produce the appearance with 
which, doubtless, everyone is familiar. 

§ 97. Clusters of Stars. — The stars are very 
irregularly distributed over the surface of the heavens. 



Star- Clusters. 123 

This is, indeed, sufficiently obvious to the unaided eye, 
and it is confirmed by the telescope. In certain 
places we have a dense aggregation of stars of so 
marked a character as to make it almost certain that 
the group must be in some way connected together, 
and that, consequently, the aggregation is real, and 
not merely apparent, as it might be if the stars were 
really only accidentally near to the same line of sight, 
and, consequently, appeared to be densely crowded 
together, when, in reality, they might be at vast dis- 
tances apart. 

Of such a group we have a very well known ex- 
ample in the group called the Pleiades, which we 
have already mentioned (§ 8). Most persons can see 
six stars in the Pleiades without difficulty, but with 
unusually acute vision more can be detected. With 
the slightest instrumental aid, however, the number is 
very greatly increased, and the group is seen to con- 
sist of perhaps 100 stars. 

Another illustration of such a group is an object 
in the constellation Cancer known as the Praesepe, or 
the Beehive. To the unaided eye this is merely a 
dullish spot on the sky, not well seen unless the night 
is very clear. A telescope shows, however, that this 
dullish spot is really an aggregation of perhaps 60 
small stars. 

By far the most splendid object of this kind in the 
northern hemisphere is the cluster in the Sword- 
handle of Perseus. We have here two groups of stars 
close together, and, when seen in a good telescope, 
the multitudes of these stars, and their intrinsic 
brightness, form a most superb spectacle. 



124 Astronomy. 

§ 98. Globular Clusters. — The objects known as 
star-clusters are exceedingly numerous. Among them 
are several which are remarkable telescopic objects, 
not for the brightness (even in the telescope) of the 
individual stars composing the star cluster, but for 
the vast numbers in which the stars are present, 
and for the closeness with which they lie together. 
These objects are often known as globular clusters, 
because the stars forming them seem to lie within a 
globular portion of space, and they frequently appear 
to be much more densely compacted together to- 
wards the centre of the globe. In fact, at the centre 
of one of these splendid objects it is in some cases 
almost impossible to discriminate the individual stars, 
so closely is their light blended. As Sir John Herschel 
says, 4 It would be a vain task to attempt to count 
the stars in one of these globular clusters. They are 
not to be reckoned by hundreds, and on a rough cal- 
culation grounded on the apparent intervals between 
them at the borders and the angular diameter of the 
whole group, it would appear that many clusters of 
this description must contain at least five thousand 
stars compacted and wedged together in a round 
space whose angular diameter does not exceed eight 
or ten minutes, that is to say, in an area not more 
than a tenth part of that covered by the moon/ 

The most remarkable of these objects in the 
northern hemisphere is the globular cluster in Hercu- 
les (Right ascension i6 h 37™. Declination + 36°43 ). 
To the unaided eye or in a small telescope this looks 
like a dull nebulous spot, and it requires a good tele- 
scope to exhibit it adequately. 



The Fixed Stars. 125 

§ 99. Telescopic Appearance of a Star. — The 

appearance of a star in a telescope differs in a most 
marked manner from the appearance of one of the 
larger planets. In the case of the planet we can see 
what is called the * disk,' we can actually observe that 
the planet appears circular and that it is presumably a 
globe with an appreciable diameter. In most cases too 
we can discern markings upon the globe of the planet 
of which drawings may be made. Indeed, as we 
have already mentioned (§ 52), we can see in the planet 
Venus changes precisely analogous to the phases of 
the moon, thus proving, of course, that the planet pos- 
sesses an appreciable disk. By increasing the mag- 
nifying power of the telescope the size of the disk can 
be increased, though, of course, at the expense of its 
intrinsic brightness. 

Widely different, however, is the telescopic appear- 
ance of a fixed star. Even the most powerful tele- 
scope only shows a star as a little point of light. By 
increasing the optical power of the telescope the bril- 
liancy of the radiation from this point can be increased, 
but no augmentation of the magnifying power has 
hitherto sufficed to show any appreciable ' disk ' in the 
great majority of the fixed stars which have been ex- 
amined. How is this to be explained ? The answer 
is to be sought not in the real minuteness of the stars 
but in the vast distances at which they are situated. 
In order to form some estimate of the real diameter 
which the stars do subtend at the eye, let us suppose 
that our sun were to be moved away from us to a dis- 
tance comparable with that by which we are sepa- 
rated from those stars which are nearest to us. 




126 Astronomy. 

For this purpose the sun would have to be trans- 
ferred to a distance not less than 200,000 times as far 
as his present distance from the earth. Let a b (fig. 
39), denote the diameter of the sun, and let e be the 

position of the earth. 
Then as we have already 
seen (§ 2), the circular 
measure of the angle 
which the sun subtends 
at the earth is practically equal toAB-fEB. Now 
suppose the sun be transferred to the position indi- 
cated by a' b' then the angle which he would subtend 
in the new position is a' b' h- e b'. 

Hence the ratio of the angles which the apparent 
diameter of the sun subtends at the eye at the two dif- 
ferent distances is 

a b _^_ a'b' 

E B EB' 

but as the real diameter of the sun is the same in both 
cases, we must have 

ab = a'b' 

and hence the ratio just written becomes 

e b' 
e B 

Hence we infer that the angle which the sun's dia- 
meter subtends at the eye varies inversely as his dis- 
tance from the observer. 

If, therefore, the sun were to be carried away from 
us to a distance 200,000 times greater than his pre- 



Variable Stars. 127 

sent distance, the angle which his diameter at present 
subtends would be diminished to the 200,000th part 
of what it is at present. Assuming as we may do for 
rough purposes that the sun's apparent diameter is 
half a degree, it follows that the apparent diameter 
when translated to the distance of a star would be 
expressed in seconds by the fraction 

1800 



200000 



= o ,/# oo9. 



In other words, the sun's diameter would then sub- 
tend an angle less than the hundredth part of a, single 
second. 

It is at present, at all events, quite out of the 
question to suppose that a quantity so minute as this 
could be detected even by the best instruments. Even 
were it ten times as great it would be barely appreci- 
able, nor unless it were at least fifty times as great 
would it be possible to measure it with any approach 
to precision. 

It is, therefore, clear that we cannot infer from the 
minute apparent size of the stars in the telescope any- 
thing with respect to their actual dimensions. 

§ 100. Variable Stars We have mentioned the 

mode of classifying stars by their magnitudes ; we 
have now to add that there are some stars to which 
this method cannot be applied. These are called 
variable stars, inasmuch as their brightness is not con- 
stant, as that of the majority of stars appears to be. 
There are some hundreds of stars in the heavens the 
brightness of which is now known to change. It would 



128 Astronomy. 

be difficult here to describe in detail the different 
classes of the variable stars, so we shall merely give a 
brief account of a few of the most remarkable. 

In the constellation Perseus is a bright star Algol 
(Right ascension 3 h o m . Declination -f 40 27'). Owing 
to the convenient situation of this star it may be seen 
every night in the northern hemisphere. Algol is 
usually of the second magnitude, but in a period of 
between two and three days, or more accurately in a 
period of 2 d 20 h 48 m 5S 8 it goes through a most re- 
markable cycle of changes. These changes commence 
by a gradual diminution of the brightness of the star 
from the second magnitude down to the fourth in a 
period of three or four hours. At the fourth magni- 
tude the star remains for twenty minutes, and then 
begins to increase in brightness again until after 
another interval of three or four hours it regains the 
second magnitude. At the second magnitude it con- 
tinues for a period of about 2 d 13 11 , when the same 
series of changes commences anew. 

Another very remarkable star belonging to the class 
of variables is o Ceti or Mira (Right ascension 2 h 13™ 
Declination — 3 3 V). The period of the changes of 
this star is 33 i d 8 h . For about five months of this 
time the star is quite invisible, it then gradually in- 
creases in brightness until it becomes nearly of the 
second or third magnitude. After remaining at its 
greatest brightness for some time it again gradually 
sinks down to invisibility. 

§101. Proper Motion of Stars. — We have hitherto 
frequently used the expression * fixed stars ; ' we have 
now to introduce a qualification which must be made 



Proper Motion of Stars. 129 

as to the use of the word fixed with reference to the 
stars. Compared with the planets, the places of which 
are continually changing upon the surface of the celes- 
tial sphere, the stars may, no doubt, be termed fixed, 
but when accurate observations of the places of the stars 
made at widely distant intervals of time are compared 
together it is found that to some of the stars the adjec- 
tive/Lxed cannot be literally applied, as it is undoubtedly 
true that they are moving. It is true that the great 
majority of what are called fixed stars do not appear 
to have any discernible motion, and, even those which 
move most rapidly, when viewed from the vast distances 
by which they are separated from the earth, appear 
to traverse but a very minute arc of the heavens in 
the course of a year. The most rapidly moving star 
does not move over an arc on the celestial sphere of 
10" per annum. A motion so slow as this is unap- 
preciable without very refined observations. The moon 
has a diameter which subtends at the eye an angle 
which we may roughly estimate at half a degree, and 
to move over a space equal to the diameter of the 
moon on the surface of the heavens would require a 
couple of centuries even for the most rapidly moving 
star. 

We have already had occasion to discriminate be- 
tween real motiDn and apparent motion (§ 46), and are 
therefore naturally tempted to inquire whether the 
motions of the stars which we have been considering 
are real, or whether they can be explained as merely 
apparent motions. Now where must we look for the 
cause of the apparent motion ? It is manifest that the 
annual motion of the earth around the sun could not 



130 Astronomy. 

possibly explain the appearances which have been 
observed. The annual motion of the earth around 
the sun would have an effect which must be clearly 
periodic in its nature. In fact, it would be merely the 
annual parallax which we have already considered 
(§71). The motions which we have to explain are not 
(so far as we know at present) of a periodical character ; 
for the stars which possess this motion usually appear 
to move continually along great circles. 

§ 102. Motion of the Sun through Space. — It was 
therefore suggested by Sir W. Herschel that possibly a 
portion of the proper motions of the stars could be 
explained by the supposition that the sun, carrying 
with it its retinue of planets, and all the other bodies 
forming the solar system, was actually moving in space. 
On this supposition, it is clear that those stars which 
were sufficiently near to us must have an apparent 
proper motion. If the motion of the sun were di- 
rected along a straight line towards a certain point of 
the heavens, then the apparent place of a star at that 
point would be unaffected by the motion of the sun ; 
but all other stars would spread away from that point 
just as when you are travelling along a straight road 
the objects on each side of the road appear to spread 
away, as it were, from the point towards which your 
journey was directed. 

It was found by Sir W. Herschel that a consider- 
able portion of the observed proper motions of the 
stars could be explained by the supposition that the 
sun was moving towards a point in the heavens near 
to the star \ Herculis. The investigations of other 
astronomers have tended to confirm this very re- 



Proper Motion of Stars. 131 

markable deduction as to the sun's motion in space, 
and have led them to conclude that the sun is moving 
towards a point of the heavens which (considering the 
difficulty of the investigation) is exceedingly close to 
the point determined by Sir W. Herschel. The right 
ascension of the point thus determined is 17 11 8 m , 
and its declination is -\- 35°. 

Not only has the direction in which the sun moves 
been determined, but the same series of observations 
serve to determine the velocity of the motion. It is 
found that in one year the sun probably moves through 
a space equal to 1*623 racm of the orbit of the earth 
around the sun. 

We thus see that the real motion of the earth 
in space is of a very complicated character ; for 
though it describes an ellipse about the sun in the 
focus, yet the sun is itself in constant motion, and 
consequently the real motion of the earth is a com- 
posite movement, partly arising from its own proper 
motion around the sun, and partly arising from the 
fact that as a member of the solar system, the earth 
partakes of the motion of the solar system in space. 

§ 103. Real Proper Motion of the Stars. — It 
should, however, be observed that after every possible 
allowance has been made for the effect of the motion 
of the solar system there remain still outstanding 
certain portions of the proper motions of the stars, 
which are only to be explained by the fact that the 
stars in question really are in actual movement. 

Nor, if we reflect for a moment, is there much in 
the last conclusion to cause surprise ? The first law of 
motion combined with the most elementary notions 

K 2 



132 Astronomy. 

of probabilities will show us how exceedingly im- 
probable rest really is. Among all the possible kinds 
©f motion, infinitely various both in regard to velo- 
city and in regard to direction, there is no one which is 
not h priori just as probable as another ; there is no one 
which is not d priori just as probable as rest. Hence 
even if there were no causes tending to produce change 
from an initial state of things it would be infinitely im- 
probable that any body in the universe was absolutely 
at rest. But even if a body were originally at rest it 
could not remain so. Distant as the stars are from 
the sun, and from each other, they must still, so far as 
we know at present, act upon each other. It is true 
that these forces acting across such vast distances 
may be slender, but great or small they are incompa- 
tible with rest, and hence we may be assured that 
every particle in the universe (with, it is conceivable, 
one exception) is in motion. 

We are thus led to believe that the fact that 
proper motion has only been detected in compara- 
tively few stars is to be attributed, not to the actual 
absence of proper motion, but rather to the circum- 
stance that the stars are so exceedingly far off that, 
viewed from this distance, the motions appear so small 
that they have not hitherto been detected. It can 
hardly be doubted that could we compare the places 
of stars now with the places of the same stars 1,000 
years ago most of them would be found to have 
changed. Unfortunately, however, the birth of accu- 
rate astronomical observation is so recent that we 
have no means of making this comparison, for the 
ancient observations which have been handed down 



Double Stars. 133 

to us are not sufficiently accurate to afford trust- 
worthy results. 

§ 104. Double Stars. — We have already alluded 
to the occasional close proximity in which stars are 
found on the celestial sphere. In many cases we 
have the phenomenon which is known as a double 
star. Two stars are frequently found which appear 
to be so exceedingly close together, that the angular 
distance by which the stars are separated is less 
than one second of arc, and an exceedingly good tele- 
scope is" required to 'divide' such an object, which, 
when viewed in an inferior instrument, would appear 
to consist only of a single star. The great majority 
of double stars known at present are, however, not 
nearly so closp together. About 10,000 objects have 
now been discovered which are included under the 
term double stars, though it must be added that the 
components of many of these are at a considerable 
distance apart. 

We shall here briefly describe a few of the most 
remarkable of these very interesting objects. 

§ 105. Castor as a Binary Star. — One of the finest 
double stars in the heavens is Castor (a Gemino- 
rum). (Right ascension 7 h 26 m . Declination + 32 
17'.) Viewed by the unaided eye the two stars 
together resemble but a single star, but in a mode- 
rately good telescope it is seen that what appears like 
one star is really two separate stars. The angular 
distance at which these two stars are separated is 
about five seconds. One of the stars is of the third 
magnitude, and the other is somewhat less. The 
reason why the unaided eye cannot distinguish the 



134 Astronomy. 

separate components is their great proximity. An 
angle of five seconds is about the same angle as that 
which is subtended by the diameter of a penny at a 
distance of about 1,200 metres, and is therefore quite 
inappreciable without instrumental aid. The question 
now arises whether the propinquity of the two stars 
forming Castor is apparent or real. This propinquity 
might be explained by the supposition that the two 
stars were really close together compared with the 
distance by which they are separated from us. Or, 
it could equally be explained by supposing that the 
two stars, though really far apart, yet appeared so 
nearly in the same line of vision that, when projected 
on the surface of the heavens, they seemed to be close 
together. It cannot be doubted that in the case of 
many of the double stars, especially those in which 
the components appear tolerably distant, the propin- 
quity is only apparent and arises from the two stars being 
near the same line of vision. But it is also undoubtedly 
true that, in the case of very many of the double stars, 
especially among those belonging to the class which 
includes Castor, the two stars are really at about the 
same distance from us, and therefore, as compared with 
that distance, they are really close together. 

Many double stars of this description exhibit a 
phenomenon of the greatest possible interest. If we 
imagine a great circle to be drawn from one of the 
two component stars to the north pole of the celestial 
sphere, then the angle between this great circle and 
the great circle which joins the two stars is termed 
the position angle of the double star. By an ingenious 
instrument called a micrometer, which is attached to 



Double Stars. 1 3 5 

the eye- end of a telescope mounted equatorially, it is 
possible to measure both the position angle of the two 
components of a double star, and also the distance of 
the two stars expressed in seconds of arc. When 
observations made in this way are compared with 
similar observations of the same double star, made 
after an interval of some years, it is found in many 
cases that there is a decided change both in the 
distance and in the angle of position. In the case of 
the double star Castor, at present under considera- 
tion, it is true that the movement is very slow. It is, 
however, undoubted that in the course of some cen- 
turies l one of the components will revolve completely 
around the other. 

§ 106. Motion of a Binary Star. — The theory of 
gravitation affords us the explanation of these changes. 
We have seen how in the case of the sun and the 
planets each planet describes around the sun an orbit 
of which the figure is an ellipse, with the sun in one 
focus, while the law according to which the velocity 
changes is defined by the fact that equal areas must 
be swept out in equal times. The circumstances pre- 
sented by the sun and a planet (the earth, for example) 
are somewhat peculiar, and Kepler's laws must be 
stated somewhat differently before they can be ap- 
plied with strict generality to the motion of a binary 
star (as one of the moving double stars is termed). 
In the case of the sun and the earth we have a com- 
paratively minute body moving around a very large 
body. In fact, as the mass of the sun is more than 

1 The periods assigned for the time of revolution of Castor 
vary from 232 years (Madler) to 996 years (Thiele). 



1 36 Astronomy. 

300,000 times greater than the mass of the earth, we 
may neglect the mass of the earth in comparison with 
the mass of the sun. Thus, in speaking of Kepler's 
laws as applied to the motion of a planet around the 
sun, we often regard the centre of the sun as a fixed 
point, and attribute all the motion which is observed 
to the planet. 

It is manifest, however, that some modification of 
Kepler's laws is necessary before we can apply them to 
the case of most of the binary stars. In the case of 
Castor, though the two components are not exactly 
equal, yet they are so nearly so that it would obvi- 
ously be absurd to regard even the larger of them 
as a fixed point while the whole orbital motion was 
performed round it by the other. The fact of the 
matter is, that both the components are in motion, each 
under the influence of the attraction of the other, and 
that what we actually observe and measure is only the 
relative motion of the components. 

It would lead us beyond the limits of this book to 
endeavour to prove the more generalised conception 
of Kepler's laws which we shall now enunciate. Let 
us suppose the case of a binary star so far removed 
from the influence of other stars or celestial bodies 
that their attraction may be regarded as insensible. 
Then each of the two components of the binary star 
is acted upon by the attraction of the other compo- 
nent, but by no other force. We suppose a straight 
line a b to be drawn connecting the centres of the 
stars, and we divide this line into two- parts, AG 
and b g, in the proportions of the masses of the two 
stars, so that the point of division g lies between the 



Double Stars. 137 

two stars and nearer to that star, a, which has the 
greater mass. The point g thus determined is the 
centre of gravity of the two stars. Now, it can be 
proved that however the stars a and b may move in 
consequence of their mutual attractions, the point 
G will either remain at rest or will move uniformly 
in a straight line. It can be shown that each of the 
stars a and b will move in an elliptic orbit around 
the point g as the focus, and that each star will de- 
scribe equal areas in equal times. 

It can also be shown that, although both of the 
stars are in motion, yet the relative motion of one 
star about the other, /.«., the morion of the star b 
about the star a as it would be seen by an observer who 
was stationed on a, is precisely the same as if the mass 
of the star a were augmented by the mass of the star 
B, and as if a were then at rest and b moved round it 
just as a planet does around the sun, To this apparent 
motion of b around a, Kepler's laws will strictly apply. 
The orbit of b is an ellipse of which a is one of the 
foci, and the radius vector drawn from a to b will 
sweep out equal areas in equal times. 

It is natural to inquire whether these theoretical 
anticipations with respect to the motions of the binary 
stars are borne out by observation. We have no 
reason to expect that we shall actually see motions 
of the simple character which we have described. It 
is to be recollected that the plane in which the orbit 
is described may be inclined in any way to the surface 
of the celestial sphere. Consequently the orbit which 
we shall see will only be the projection of the real 
orbit upon a plane which is perpendicular to the line 



138 Astronomy. 

joining the binary star to the eye. We have there- 
fore to consider what modifications the orbit may 
undergo by projection. It can be shown that if the 
original orbit be elliptic, the projected orbit will be 
elliptic also ; but it also appears that though the star 
a was the focus of the original orbit, it would not be 
the focus of the projected orbit. The law of the de- 
scription of equal areas in equal times would hold 
equally true both in the original orbit and in the pro- 
jected orbit. 

By a comparison of observations made at dif- 
ferent times it is possible to plot down the actual 
position of the star b with respect to the star a, at the 
corresponding dates. It is found that in the case of 
several binary stars the orbit thus formed is elliptic, 
and it is possible, by a consideration of the position 
of the point a in this ellipse, to determine the position 
of the true orbit with reference to the celestial sphere 
and the various circumstances connected with the 
motion. 

In this way the true orbits of several of the most 
remarkable among the binary stars have been deter- 
mined. Of these stars the most rapid in its movements 
appears to be 42 Comae Berenices, which accomplishes 
its revolution in a period of 257 years. The two com- 
ponents of this star are exceedingly close together, the 
greatest distance being about one second of arc. 
There is very great difficulty in making accurate 
measurements of a double star so close as this one. 
Consequently more reliance may be placed upon the 
determination of the orbits of other binary stars, the 
components of which are farther apart than those of 



Double Stars. 1 39 

42 Comae Berenices. Among these we may mention a 
very remarkable binary star £ Ursae Majoris. The dis- 
tance of the two components of this star varies from 
one second of arc to three seconds. The first recorded 
observation of the distance and position angle of this 
star was by Sir W. Herschel in 1781, and since that 
date it has been repeatedly observed. From a compari- 
son of all the measurements which have been made it 
appears that the periodic time of the revolution of one 
component of £ Ursae about the other is 60 years, 
and it is exceedingly improbable that this could be 
erroneous to the extent of a single year. Thus this 
star has been observed through more than one entire 
revolution. 

§ 107. Dimensions of the Orbit of a Binary Star. 
— In the determination of the size of a binary star all 
we can generally ascertain is, of course, the diameter of 
the orbit as measured in seconds of arc. Actually to de- 
termine the number of kilometres in the diameter of 
the orbit, it would be further necessary for us to know 
the distance at which the binary star is from the earth. 
This distance is, in the great majority of cases, entirely 
unknown to us at present. There are, however, one 
or two exceptions. Of these we shall mention 
Sirius. 

Early in the present century the proper motion of 
this star was found to be affected by an irregularity 
which showed that an unseen body must be moving 
around it and disturbing its motion by its attraction. 
After a hundred years of observation the orbit of this 
body was calculated, and it was shown that the irregu- 
lar motion of Sirius could be accounted for by sup- 



140 Astronomy. 

posing that the disturbing satellite had a period o! 
about 50 years. This satellite was actually discovered 
by Alvan Clark, in 1862, and found to be moving 
around Sirius at a mean angular distance of about 
seven seconds. Now the annual parallax of Sirius 
is found to be o"*2 5, that is to say the radius of the 
earth's orbit viewed from the distance of Sirius 
subtends an angle of o"*2 5. It therefore follows 
that the real distance of the companion of Sirius 
must exceed the distance of the earth from the sun 
in the ratio that 7" exceeds o"*25, that is, it is 28 
times as great. 

§ 108. Determination of the Mass of a Binary 
Star. — When we know the diameter of the orbit of 
a binary star and its periodic time we are able to 
compute the sum of the masses of the two com- 
ponent stars. This is an exceedingly interesting 
subject, inasmuch as it affords us a method of com- 
paring the importance of the stars, as far as mass is 
concerned, with the importance of our sun. 

Let us first consider what the periodic time of 
a planet would be if it revolved round the sun in 
an orbit of which the radius were 28 times that of 
the earth's orbit. According to Kepler's third law, 
the square of the periodic time is proportional to 
the cube of the distance ; consequently, since the 
earth revolves around the sun in one year, it follows 
that a planet such as we have supposed would re- 
volve around the sun in a period of time which was 
equal to the square root of the cube of 28 i.e. to 148 
years very nearly. 

According to the latest results it would appeal 



Double Stars. 141 

that the periodic time of the revolution of the satel- 
lite of Sirius is 49*3 years, i.e. the velocity with 
which the motion takes place is greater than it 
would be if the mass of Sirius equalled the mass of 
the sun. 

We shall now show how the ratio of the mass of 
the sun (augmented, it should in strictness be said, 
by the mass of the earth) to that of Sirius and its 
satellite, taken together, can be ascertained. For 
this we require the following principle, which for the 
present we shall take for granted. 

If two bodies, a and b, are revolving in conse- 
quence of their mutual attractions, then the sum of 
the masses is inversely proportional to the square of 
the periodic time, supposing the mean distance of A 
and B to remain unaltered. 

It therefore appears that the following proportion 
is true : 

Mass of Sun and Earth / 49*3 V 

Mass of Sirius and Satellite ~~ \ 148 / 

It follows from this that if we regard the mass of 
our sun as 1, the mass of Sirius and its satellite is 
about 9 times that of the sun. 

Now, though it is true that subsequent observa- 
tions may necessitate corrections in these results, 
yet we may be pretty confident that the mass of 
Sirius is several times as great as that of our sun. 
The most uncertain part of the data is the annual par- 
allax of Sirius, which has not yet been certainly deter- 
mined, and may deviate from o".25 by 50 per cent., 
or more, of its amount. 



142 Astronomy. 

§ 109. Colours of Double Stars. — Among the 
most pleasing and remarkable phenomena presented 
by double stars are the beautiful colours which they 
often present. The effect is occasionally heightened 
by the circumstance that the colours of the two com- 
ponents are frequently not only different but are con- 
trasted in a marked manner. Conspicuous among 
these objects is a very beautiful double star y Andro- 
medae. The two components of this star are orange 
and greenish blue. Attentive examination with a 
powerful telescope shows also that the greenish blue 
component consists of two exceedingly small stars close 
together. While considering this subject it should be 
remarked that isolated stars of a more or less reddish 
hue are tolerably common in the heavens, the cata- 
logues containing some four or five hundred stars of 
this character. Among those visible to the naked 
eye perhaps the most conspicuous is the bright star a 
Orionis. Stars of a greenish or bluish hue are much 
less common, and it is very remarkable that, with very 
few exceptions, a star of this colour is not found 
isolated, but always occurs as one of the two compo- 
nents of a ' double star.' 



CHAPTER XIX. 

NEBULAE. 



§ no. Nebulae. — There are a great number and 
variety of objects in the heavens which are known 
under the general term of ' Nebulae.' The great ma* 



Nebula. 143 

jority of these objects are invisible to the naked eye, 
but with the aid of powerful telescopes some thou- 
sands of such objects have been already discovered. 
Of these objects, which for convenience are grouped 
together, many are undoubtedly mere clusters of stars 
such as those of which we have already given some 
account. It is, nevertheless, tolerably certain that 
many of the objects termed nebulae are not to be 
considered as mere clusters of stars, though their 
real nature has, as yet, been only partially deter- 
mined. 

§ in. Classification of Nebulae. — The following 
analysis } of the different objects, which are generally 
classed under the name of nebulae, has been made by 
Sir William Herschel, to whom the discovery of a 
vast number of nebulae is due : — 

1. Clusters of stars, in which the stars are clearly 
distinguishable ; these are again divided into globular 
and irregular clusters. 

2. Resolvable nebulae, or such as excite a sus- 
picion that they consist of stars, and which any in- 
crease of the optical power of the telescope may be 
expected to resolve into distinct stars. 

3. Nebulae, properly so called, in which there is 
no appearance whatever of stars, which again have 
been subdivided into subordinate ones, according to 
their brightness and size. 

4. Planetary nebulae. 

5. Stellar nebulae. -. 

6. Nebulous stars. 

1 Sir John Herschel's Outlines of Astronomy. 



144 Astronomy. 

The first of these classes is that which we have 
already described (§§ 97, 98) ; the resolvable nebulae, 
which form the second class, are to be regarded as 
clusters of stars, which are either too remote from us, 
or the individual stars of which are too faint to enable 
them to be distinguished. Among the most remark- 
able objects at present under consideration are the 
oval nebulae. They are of all degrees of eccentricity, 
some being nearly circular, while others are so elon- 
gated as to form what have been called ' rays.' The 
finest object of this class is the well-known nebula in 
the girdle of Andromeda. This object is just visible 
to the naked eye as a dullish spot on the heavens. 
Viewed in a powerful telescope it is seen to be a 
nebula about 2^° in length, and i° in breadth. It 
thus occupies a region on the heavens five times as 
long and twice as broad as the diameter of the full 
moon. The marginal portions are faint, but the 
brightness gradually increases towards the centre, 
which consists of a bright nucleus. This nebula has 
never actually been resolved, though it is seen to con- 
tain such a multitude of minute stars that there can 
be little doubt that with suitable instrumental power, 
it would be completely resolved. 

Among the rarest, and indeed the most remarkable, 
nebulae are those which are known under the name of 
the 'Annular Nebulae.' The most conspicuous of 
these is to be found in the constellation Lyra ; it con- 
sists of a luminous ring ; but (as Sir John Herschel 
remarks) the central vacuity is not quite dark, but is 
filled in with faint nebulae 'like a gauze stretched over 
a hoop.' 



Nebula. 145 

Planetary Nebulae are very curious objects 5 they 
derive their name from the fact that, viewed in a good 
telescope they appear to have a sharply defined more 
or less circular disk, immediately suggesting the appear- 
ance presented by a planet. These objects are gene- 
rally of a bluish or greenish hue. Their apparent 
diameter is small ; the largest of them is situated in 
Ursa Major, and the area it occupies on the heavens 
is less than one hundredth part of the area occupied 
by the full moon. Still the intrinsic dimensions of 
the object must be great indeed. If it were situated 
at a distance from us not greater than that of 61 
Cygni, the diameter of the globe which it occupies 
would be seven times greater than the diameter of the 
orbit of the outermost planet of our system. 

Among the class of Stellar Nebulae one of the 
most superb objects visible in the heavens must be 
included. The object to w T hich we refer is the great 
nebula in the Sword-handle of the constellation of 
Orion. The star 6 Orionis consists of four pretty 
bright stars close together, while in a good telescope 
at least two others are visible, the whole presenting 
the almost unique spectacle of a sextuple star. But 
around this star, and extending to vast distances on 
all sides of it is the great nebula in Orion. The most 
remarkable feature of this nebula is the complexity 
of detail which it exhibits. The light is of a slightly 
bluish hue, and under the great power of Lord Rosse's 
telescope portions of it are seen to be undoubtedly 
composed of stars. Perhaps it would be more correct 
to say that portions of it contain stars ; for, as we shall 

L 



146 Astronomy. 

presently show, there is good reason to believe that in 
this nebula, as well as in some others, a part of the 
light which we receive is due to glowing gas. 

The last of the different kinds of nebulae to which 
we shall allude is the class of objects known as nebu- 
lous stars. By a ' nebulous star ' we are to under- 
stand a star surrounded by a luminous haze, which is, 
however, generally so faint as only to be visible in 
powerful instruments. 



CHAPTER XX. 

SPECTRUM ANALYSIS. 



§ 112. Composition of Light. — We shall now give 
some account of a very remarkable method which has 
recently been applied with great success to the exami- 
nation of the heavenly bodies. This method is termed 
spectrum analysis. The peculiar feature of spectrum 
analysis is, that with the assistance of a telescope it 
actually gives us information as to the nature of the 
elementary substances which are present in some of 
the celestial bodies. To explain how this is accom- 
plished it will be necessary for us to describe briefly 
some properties of light. 

A ray of ordinary sunlight consists in reality of a 
number of rays of different colours blended together. 
The ' white ' colour of ordinary sunlight is due to the 
joint effect of the several different rays. We have, 
however, the means of separating the constituent rays 



Spectrum Analysis. 147 

of a beam of light and examining them individually. 
This is due to the circumstance that the amount of 
bending which a ray of light undergoes when it passes 
through a prism varies with the colour of the light. 

§ 113. Construction of the Spectroscope. — Sup- 
pose a b c, fig. 40, to represent a prism of flint glass. 
If a ray of ordinary white light travelling along the 
direction p q falls upon the prism at Q, it is bent by 
refraction so that the direction in which it traverses 
the prism is different from the direction in which it 
was moving when it first encountered the prism. The 




amount of the bending is, how r ever, dependent upon 
the colour of the light. In a beam of white light we 
have blended together the seven well-known prismatic 
colours, viz., red, orange, yellow, green, blue, indigo, 
violet. We shall trace the course of the first of these 
and the last. The red light is the least bent ; it tra- 
vels along (let us suppose) the direction q r until it 
meets the second surface of the prism at R ; it is then 
again bent at emergence, and finally travels along the 
direction r s. On the other hand, the violet portion 
cf the incident beam, which originally travelled along 

L2 



148 



Astronomy. 



the direction p q, is more bent at each refraction than 
the red rays. Consequently after the first refraction 
it assumes the direction Q r', and after the second re- 
fraction, the direction r' s'. The intermediate rays of 
orange, yellow, green, blue, and indigo, after passing 
the prism, are found to be more refracted than the 
red rays, and less refracted than the violet rays ; they 
are, therefore, found in the interval between the lines 
r s and r' s'. 

We have therefore, in the prism, a means of decom- 
posing a ray of light and examining the different cons- 
tituents of which it is made. We shall now show how 
this is practically applied in the instrument known as 
the spectrosco/e. The principle of this instrument may- 
be explained by reference to fig. 41. At s is a narrow 

slit, which is supposed 
to be perpendicular to 
the plane of the paper. 
Through this slit a thin 
line of light passes, and 
it is this thin line of 
it light which is to be 
examined in the spec- 
troscope. After pass- 
ing through s, the light 
diverges until it falls 
upon an achromatic lens 
placed at a. This lens is to be so placed that the 
distance a s is equal to the focal length of the lens ; 
it therefore follows that the beam diverging from s, 
will, after refraction through the lens a, emerge as 
a beam of which all the constituent rays are parallel. 



Fig. 41. 




Spectrum Analysis. 149 

Let us now for a moment fix our attention upon the 
rays of some particular colour. Suppose, for example, 
the red rays. The parallel beam of red rays will fall 
upon the prism p. Now, since each of these rays has 
the same colour, it will, on passing through the prism, 
be deflected through the same angle, and therefore, 
the beam which consisted of parallel rays before in- 
cidence upon the prism will "consist of parallel rays 
after refraction through the prism, the only difference 
being that the entire system of parallel rays will be 
bent from the direction which they had before. In 
this condition the rays will fall upon the achromatic 
lens b, which will bring them to a focus at a point 
«r, where we shall suppose a suitable screen to be 
placed. Thus the red rays which pass through the 
slit at s will form a red image of the slit upon the 
screen at r. 

But what will be the case with the violet consti- 
tuents of the light which passes through s? The 
violet rays will fall upon the lens a, and will emerge as 
a parallel beam (for we have supposed the lenses a and 
b to be both achromatic), the parallel violet beam will 
then fall upon p, and it will emerge from p also as a 
beam of parallel rays. It will, however, be more de- 
flected than the beam of red rays, but still not so much 
so as to prevent it falling upon the lens b, which will 
make it converge so as to form an image at t near to 
the red image at r, but somewhat below it. 

Now let us suppose the slit at s to be exceedingly 
narrow, and let us suppose that the beam of light 
which originally passed through s contained rays of 
every degree oi refrangibility from the extreme red to the 



J So Astronomy. 

extreme violet. We should then have on the screen 
an indefinitely great number of images of the slit in 
different hues, and these images would be so ex- 
ceedingly close together that the appearance pre- 
sented would be a band of light equal in width to the 
length of the image of the slit, and extending from 
R to T. This band, the colour of which gradually 
changes from red at R to violet at t, is known as the 
prismatic spectrum. Instead of the screen the eye it- 
self may be employed to receive the light which 
emerges from the lens b, so that the spectrum is im- 
pressed upon the retina. For the more delicate pur- 
poses of spectrum analysis this plan is always adopted. 

Suppose, now, that the light which was being ex- 
amined consisted only of rays of certain special refran- 
gibilities, the spectrum which would be produced would 
then only show images of the slit corresponding to the 
particular rays which were present in the beam. Con- 
sequently, the spectrum would be * interrupted/ and 
the character of the spectrum would reveal the nature 
of the light of which the beam was composed. 

This may be made to give us most valuable in- 
formation with reference to the nature of the source 
from which the light emanates. We do not here 
attempt to enter into the matter further than is neces- 
sary to show how the method can be applied astrono- 
mically. When the light from some of the nebulae 
(especially those of a bluish hue) was examined in the 
spectroscope it was found by Huggins that by far the 
greater portion of the light is concentrated into two 
or three bright lines. This proves that a great portion 
of the light from nebulae of this particular character 



Spectrum A nalysis. 151 

consists of rays possessing the special refrangibilities 
corresponding to the observed rays. 

We have thus an accurate means of comparing 
the light which comes from the nebulae with the 
light from other sources. If a glass tube contain a 
small quantity of gas, and if a galvanic current be 
passed through the tube (we do not here attempt to 
enter into details) the gas inside the tube may be 
raised to a temperature so exceedingly high that it 
will become luminous, and the light which emanates 
from it can be examined by means of the spectroscope. 
It is found that each different kind of gas yields light 
which in the spectrum forms lines of so marked a 
character as to make the spectrum characteristic ot 
the gas. It has thus been discovered by Huggins that 
the light from several of the nebulae brings evidence 
that in some of these distant objects substances are 
present with which we are familiar on the earth. He 
has thus found that there is excellent reason to believe 
that several of the nebulae are at least partially com 
posed of glowing gaseous material, and that among 
their constituents are to be found hydrogen and 
nitrogen, which are both elements of much importance 
on the earth. 

Spectrum analysis has also been applied with suc- 
cess to the examination of the light from the sun as 
well as from the fixed stars. To consider this applica- 
tion it would, however, be necessary for us to enter 
more extensively into the subject than our space 
admits. Suffice it to say, that it has been ascertained, 
by the aid of spectrum analysis, that the majority 
of the fixed stars are probably bodies of the same 



152 Astronomy. 

general character as our sun, but with individual 
peculiarities, and that in the sun and in several of the 
stars we have been able to ascertain the existence of 
several elementary substances which are present c.u 
the earth. 



INDEX, 



ANDROMEDA, nebula in, 145 
Angles, measurement of, 1 

measurement of in circular meas- 
ure, 4 
Arc, 6 
Axis of rotation, permanency of an, 

102 
Azimuth, error of, 23 

CANCER, tropic of, 114 
Capricorn, tropic of, 114 
Castor as a binary star, 133 
Circle, arctic, 113 

antarctic, 114 

graduated, 21 

great, 6 

small, 6 

meridian, 33 
Clock, astronomical, 25 

movement, 13 

rate of, 26 

sidereal, setting of, 48 
Clusters, globular, 124 
Colatitude. 31, 38 
Collimation, axis of, 21 

error of, 22 
Comets, motion of, 81 
Constellations, 8 
Culmination, upper, 31 

lower, 31 

DAY, apparent solar, 52 

mean solar, 53 

mean solar, determination of, 53 

sidereal, 24, 46 
Degree, 1, 2 
Declination, 19, 28 
Distance, polar, 29 

EARTH, a sphere, 15 

equator of, 29 

figure of, 16 

gravitation of, 75 
Earth, orbit of, nearly circular, 63 

really a planet, 62 

rotation of, 17 
Ecliptic. 45 

is at rest, 97 

obliquity of, 45 

to determine, 99 



Equator, celestial, 28 

Earth's, 29, 114 
Equinox, vernal, 45 
Equinoxes, 45 

precession of, 96 

precession of, cause of the, 103 
Ellipses, 71 

to draw, 72 

FIXED stars, parallax of, 90 

GLOBE, celestial, 14 
Graduated circle, 2 
Gravitation, the law of, 75 

towards the sun, 76 
Great Bear. 9 

Circle, 6 

HORIZON, apparent, 8 
KEPLER'S laws, 7 i 

LATITUDE, 29 

determination of, 41 
Level, error of, 23 
Light, aberration of, 107 

composition of, 146 

determination of velocity of, 109 
Line, horizontal, 8 

MAGNITUDE, first, 121 
Mars, apparent motion of, 69 
Mercury, apparent motion of, 62 

orbit of, 68 
Meridian, 23 

circle, 33 
Milky Way, 122 
Minute, 1 

Moon, distance of from Earth, 82 
Motion, apparent, 17 

apparent annual, 44 

of the heavens, apparent diurnal, 
7 

apparent diurnal of heavenly 
bodies, 11 

Earth, shape of, connected with 
the diurnal rotation, 18 

real, 17 

NADIR, 8 



154 



Index. 



NADIR, observation of, 34 
Nebulae, 142 

annular, 144 

classification of, 143 

in Andromeda, 144 

in Sword Handle of Orion, 145 

planetary, 143, 145 

resolvable, 143, 144 

stellar, 143, 145 
Neptune, 120 

PARALLAX, 82 

annual, of a star, 91 

determination of difference ofj 

of two stars, 93 
Plane, horizontal, 8 
Planets, 59, 118 

explanation of motion of, in a 
circular orbit, 78 

motion of, in an ellipse, 80 

orbits of, 71 
Pleiades, 10 

_ observation of, 43 
Pointers. 9 
Pole, 11' 

celestial, motion of, 98 

motion of among the stars, 100 

of the Earth, 101 

south, 12 

star, 9, 12 
Prsesepe, 123 
Prismatic spectrum, 150 
Protractor, 3 

RADIAN, 4 

Rate, clock's, 26 
Refraction, 38 

atmospheric, 38 

amount of, 40 

calculation of, 40 
Right ascension, 19 
Right ascensions, determination of, 27 

alterations in, of stars, 96 

SATURN, 119 

Seasons, changes of, 112 

Second, 1 

Signs of the Zodiac, 45 

Small circle, 6 

Solar system, 116 

Spectroscope, construction of, 147 

Spectrum, analysis, 146 

prismatic, 150 
Sphere, 6 

Spherical triangle, 7 
Stars, 8 

alterations in right ascensions of, 
96 



\ 



T 61? 



Stars, binary, determination of mass 

of, 140 
binary, dimensions of the orbit 

.of, 139 
binary, motion of, 135 
circumpolar, 31 
cluster of in Sword Handle of 

Perseus, 123 
clusters of, 122, T43 
declination of, 28 
distance of, 95 
double, 133 
double, colors of, 142 
the fixed, 90, 120 
fixed, parallax of, 90 
magnitudes of, 120 
nebulous, 143, 146 
numbers of, 121 
proper motion of, 94, 128 
real proper motion of, 131 
right ascension of, 28 
telescopic appearance of, 125 
variable, 127 
Sun, apparent motion of, 42 

distance of from earth, 85, 89 

the mean, 53 

motion of through space, 130 

TELESCOPE, equatorial, 11 
Time, mean, 51 

determination of mean at a given 

longitude, 57 
mean at apparent noon, 53 
mean, determination of from 

sidereal time, 57 
mean solar, 52 
sidereal, 25, 46 

sidereal, determination of at 
mean noon, 55 
Transit instrument, 20 

instrument, adjustment of, 21 

URANUS, 120 

VENUS, effect of motion of earth 
on appearance of, 67 

motion of the planet, 61 

orbit of, 63 

transit of. 85 

telescopic appearance of, 65 
Vernal equinox, 26 

YEAR, to determine length of, 59 

ZENITH, 8 

distance, 37 
distance, apparent, 38 
distance, real, 38 



